Articles

• Di Nunno, Giulia & Gianin, Emanuela Rosazza (2024). Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs. SIAM Journal on Financial Mathematics. ISSN 1945-497X. 15(2), p. 399–435. doi: 10.1137/23M1546804.
• Savku, Emel (2024). Deep-Control of Memory via Stochastic Optimal Control and Deep Learning. In Martinez, Viktor Gayoso; Queiruga-Dios, Araceli; Martin-Vaquero, Jesus; Yilmaz, Fatih; Rasteiro, Deolinda & Mierlus-Mazilu, Ion (Ed.), Mathematical Methods for Engineering Applications ICMASE 2023, Madrid, Spain, July 12–14. Springer Nature. ISSN 978-3-031-49217-4. p. 219–240. doi: 10.1007/978-3-031-49218-1_16.
• Tymoshenko, Olena; Proske, Frank Norbert & Orlovskyi, Igor (2024). Long-time behaviors of some stochastic differential equations driven by Lévy noise. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2402.05594.
• Vorobeva, Ekaterina; Eggen, Mari Dahl; Midtfjord, Alise Danielle; Benth, Fred Espen; Hupe, Patrick & Brissaud, Quentin [Show all 8 contributors for this article] (2024). Estimating stratospheric polar vortex strength using ambient ocean-generated infrasound and stochastics-based machine learning. Quarterly Journal of the Royal Meteorological Society. ISSN 0035-9009. doi: 10.1002/qj.4731. Full text in Research Archive Show summary

  There are sparse opportunities for direct measurement of upper stratospheric winds, yet improving their representation in subseasonal-to-seasonal prediction models can have significant benefits. There is solid evidence from previous research that global atmospheric infrasound waves are sensitive to stratospheric dynamics. However, there is a lack of results providing a direct mapping between infrasound recordings and polar-cap upper stratospheric winds. The global International Monitoring System (IMS), which monitors compliance with the Comprehensive Nuclear-Test-Ban Treaty, includes ground-based stations that can be used to characterize the infrasound soundscape continuously. In this study, multi-station IMS infrasound data were utilized along with a machine-learning supported stochastic model, Delay-SDE-net, to demonstrate how a near-real-time estimate of the polar-cap averaged zonal wind at 1-hPa pressure level can be found from infrasound data. The infrasound was filtered to a temporal low-frequency regime dominated by microbaroms, which are ambient-noise infrasonic waves continuously radiated into the atmosphere from nonlinear interaction between counter-propagating ocean surface waves. Delay-SDE-net was trained on 5 years (2014–2018) of infrasound data from three stations and the ERA5 reanalysis 1-hPa polar-cap averaged zonal wind. Using infrasound in 2019–2020 for validation, we demonstrate a prediction of the polar-cap averaged zonal wind, with an error standard deviation of around 12 m·s compared with ERA5. These findings highlight the potential of using infrasound data for near-real-time measurements of upper stratospheric dynamics. A long-term goal is to improve high-top atmospheric model accuracy, which can have significant implications for weather and climate prediction.

• Benth, Fred Espen; Schroers, Dennis & Veraart, Almut E.D. (2024). A feasible central limit theorem for realised covariation of SPDEs in the context of functional data. The Annals of Applied Probability. ISSN 1050-5164. 34(2), p. 2208–2242. doi: 10.1214/23-AAP2019.
• Amine, Oussama; Baños, David & Proske, Frank Norbert (2024). C∞-Regularization by Noise of Singular ODE’s. Journal of Dynamics and Differential Equations. ISSN 1040-7294. doi: 10.1007/s10884-024-10355-w.
• Grochowicz, Aleksander; van Greevenbroek, Koen & Bloomfield, Hannah C. (2024). Using power system modelling outputs to identify weather-induced extreme events in highly renewable systems. Environmental Research Letters. ISSN 1748-9326. 19(5), p. 1–15. doi: 10.1088/1748-9326/ad374a. Full text in Research Archive
• Ren, Panpan; Tang, Hao & Wang, Feng-Yu (2024). Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations. Potential Analysis. ISSN 0926-2601. doi: 10.1007/s11118-023-10113-5.
• Pilipenko, Andrey; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2024). Low-dimensional Cox-Ingersoll-Ross process. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2023.2300291. Full text in Research Archive
• Yurchenko-Tytarenko, Anton & Di Nunno, Giulia (2024). Power law in Sandwiched Volterra Volatility model. Modern Stochastics: Theory and Applications (MSTA). ISSN 2351-6046. 11(2), p. 169–194. doi: 10.15559/24-VMSTA246. Full text in Research Archive
• Compagnoni, Enea; Orvieto, Antonio; Kersting, Hans; Proske, Frank Norbert & Lucchi, Aurelien (2024). SDEs for Minimax Optimization. Proceedings of Machine Learning Research (PMLR). ISSN 2640-3498. 206.
• Grochowicz, Aleksander; Benth, Fred Espen & Zeyringer, Marianne (2024). Spatio-temporal smoothing and dynamics of different electricity flexibility options for highly renewable energy systems—Case study for Norway. Applied Energy. ISSN 0306-2619. 356. doi: 10.1016/j.apenergy.2023.122338. Show summary

  In this article, we investigate the mismatch of renewable electricity production to demand and how flexibility options enabling spatial and temporal smoothing can reduce risks of variability. As a case study we pick a simplified (partial) 2-region representation of the Norwegian electricity system and focus on wind power. We represent regional electricity production and demand through two stochastic processes: the wind capacity factors are modelled as a two-dimensional Ornstein–Uhlenbeck process and electricity demand consists of realistic base load and temperature-induced load coming from a deseasonalised autoregressive process. We validate these processes, that we have trained on historical data, through Monte Carlo simulations allowing us to generate many statistically representative weather years. For the investigated realisations (weather years) we study deviations of production from demand under different wind capacities, and introduce different scenarios where flexibility options like storage and transmission are available. Our analysis shows that simulated loss values are reduced significantly by cooperation between regions and either mode of flexibility. Combining storage and transmission leads to even more synergies and helps to stabilise production levels and thus reduces likelihoods of inadequacy of renewable power systems.

• Amine, Oussama; Baños, David Ruiz & Proske, Frank Norbert (2024). C-infinity-regularization by Noise of Singular ODE's. Journal of Dynamics and Differential Equations. ISSN 1040-7294. Full text in Research Archive
• Øksendal, Bernt Karsten (2023). Space-time stochastic calculus and white noise. In Morel, Jean-Michel & Teissier, Bernard (Ed.), Mathematics Going Forward - Collected Mathematical Brushstrokes. Springer. ISSN 978-3-031-12243-9. p. 629–649. Full text in Research Archive
• Sande, Åsmund Hausken (2023). Convex environmental contours for non-stationary processes. Ocean Engineering. ISSN 0029-8018. 292. doi: 10.1016/j.oceaneng.2023.116615. Full text in Research Archive
• Banos, David Ruiz; Sande, Åsmund Hausken & Sgarra, Carlo (2023). Guaranteed Minimum Maturity Benefits in a Self-Exciting Stochastic Mortality Model: Pricing, Estimation and Calibration. North American Actuarial Journal (NAAJ). ISSN 1092-0277. doi: 10.1080/10920277.2023.2254836. Full text in Research Archive
• Bogso, Antoine-Marie; Menoukeu-Pamen, Olivier & Proske, Frank Norbert (2023). EXISTENCE OF STRONG SOLUTIONS OF FRACTIONAL BROWNIAN SHEET DRIVEN SDES WITH INTEGRABLE DRIFT. . arXiv.org. ISSN 2331-8422.
• Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2023). Optimal control of SPDEs driven by time-space Brownian motion . arXiv.org. ISSN 2331-8422.
• Compagnoni, Enea; Biggio, Luca; Orvieto, Antonio; Proske, Frank Norbert; Kersting, Hans & Lucchi, Aurelien (2023). An SDE for Modeling SAM: Theory and Insights. Proceedings of Machine Learning Research (PMLR). ISSN 2640-3498. 202, p. 25209–25253. Full text in Research Archive
• Huseby, Arne Bang (2023). Environmental contours and time dependence. In Brito, Mario P.; Aven, Terje; Baraldi, Piero; Cepin, Marko & Zio, Enrico (Ed.), ESREL 2023 - Proceedings of the 33rd European Safety and Reliability Conference : The Future of Safety in the Reconnected World, 3 – 7 September 2023, University of Southampton, United Kingdom. Research Publishing Services. ISSN 978-981-18-8071-1. p. 1295–1302. doi: 10.3850/978-981-18-8071-1_P048-cd. Show summary

  Environmental contours are widely used as a basis for e.g., ship design. Such contours are typically used in early design when the strength and failure properties of the object under consideration are not known. An environmental contour describes the tail properties of some relevant environmental variables, and is used as input to the design process. A methodology for constructing environmental contours based on the Rosenblatt transformation has beed used extensively. More recently alternative approach where environmental contours are constructed using Monte Carlo simulation have been developed. Typically, the strength of a structural design is chosen so that the expected return period of a failure event exceeds the desired lifetime of the structure. If time dependence in the environmental variables is neglected, the expected return period is simply the inverse of the failure probability. In a more realistic model, however, such dependence should be included. In this paper we describe a method for constructing an environmental contour where time dependence is taken into account. The method is illustrated with a simple numerical example.

• Agram, Nacira & Øksendal, Bernt Karsten (2023). The Donsker delta function and local time for McKean–Vlasov processes and applications. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2023.2286252. Full text in Research Archive
• Benth, Fred Espen; Detering, Nils & Galimberti, Luca (2023). Pricing options on flow forwards by neural networks in a Hilbert space. Finance and Stochastics. ISSN 0949-2984. 28, p. 81–121. doi: 10.1007/s00780-023-00520-2.
• Giordano, Michele & Yurchenko-Tytarenko, Anton (2023). Optimal control in linear-quadratic stochastic advertising models with memory. Decisions in Economics and Finance (DAF). ISSN 1593-8883. doi: 10.1007/s10203-023-00409-x. Full text in Research Archive
• Dordevic, Jasmina (2023). Backward Doubly Stochastic Integral Equations of the Volterra Type and Some Related Problems. Communications in Mathematics and Statistics. ISSN 2194-6701. doi: 10.1007/s40304-023-00349-3. Full text in Research Archive
• Catellier, Rémi & Harang, Fabian Andsem (2023). Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation. Annales de l'I.H.P. Probabilites et statistiques. ISSN 0246-0203. 59(3), p. 1572–1609. doi: 10.1214/22-AIHP1302. Full text in Research Archive Show summary

  Existence and uniqueness of solutions to the stochastic heat equation with multiplicative spatial noise is studied. In the spirit of pathwise regularization by noise, we show that a perturbation by a sufficiently irregular continuous path establish wellposedness of such equations, even when the drift and diffusion coefficients are given as generalized functions or distributions. In addition we prove regularity of the averaged field associated to a Lévy fractional stable motion, and use this as an example of a perturbation regularizing the multiplicative stochastic heat equation.

• Di Nunno, Giulia; Kubilius, Kestutis; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2023). From Constant to Rough: A Survey of Continuous Volatility Modeling. Mathematics. ISSN 2227-7390. 11(19). doi: 10.3390/math11194201. Full text in Research Archive Show summary

  In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

• Amine, Oussama; Baghery, Karim; Pindado, Zaira & Ràfols, Carla (2023). Simulation extractable versions of Groth’s zk-SNARK revisited. International Journal of Information Security. ISSN 1615-5262. 23, p. 431–445. doi: 10.1007/s10207-023-00750-7. Full text in Research Archive
• Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2023). Parameter Estimation in Rough Bessel Model. Fractal and Fractional. 7(7). doi: 10.3390/fractalfract7070508. Full text in Research Archive
• Tang, Hao (2023). On the stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise. Journal of Functional Analysis. ISSN 0022-1236. 285(9). doi: 10.1016/j.jfa.2023.110075. Full text in Research Archive
• Benth, Fred Espen & Lempa, Jukka (2023). Hedging temperature risk with CDD and HDD temperature futures. Applied Stochastic Models in Business and Industry. ISSN 1524-1904. doi: 10.1002/asmb.2815. Full text in Research Archive
• Bordin, Chiara; Mishra, Sambeet & Benth, Fred Espen (2023). Pedagogical Perspectives of Interdisciplinary Teaching and Research: An Energy System Modelling Outlook in Relation to Energy Informatics. Energies. ISSN 1996-1073. 16(15). doi: 10.3390/en16155757. Full text in Research Archive
• Puica, Mihaela-Alexandra & Benth, Fred Espen (2023). A spatio-temporal model for predicting wind speeds in Southern California. Communications in statistics. Case studies, data analysis and applications.. ISSN 2373-7484. 9(3), p. 321–349. doi: 10.1080/23737484.2023.2217137.
• Coffie, Emmanuel; Mao, Xuerong & Proske, Frank Norbert (2023). On the Analysis of Ait-Sahalia-Type Model for Rough Volatility Modelling. Journal of theoretical probability. ISSN 0894-9840. doi: 10.1007/s10959-023-01269-2. Full text in Research Archive
• Savku, Emel (2023). A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes. Mathematics. ISSN 2227-7390. 11(14). doi: 10.3390/math11143043. Full text in Research Archive
• Benth, Fred Espen; Deelstra, Griselda & Kozplnar, And Sinem (2023). Pricing energy quanto options in the framework of Markov-modulated additive processes. IMA Journal of Management Mathematics. ISSN 1471-678X. 34(1), p. 187–220. doi: 10.1093/imaman/dpab032.
• Makhlouf, K.; Agram, Nacira; Hilbert, A. & Øksendal, Bernt Karsten (2023). SPDEs with space interactions and application to population modelling. ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV). ISSN 1292-8119. 29. doi: 10.1051/cocv/2023010. Full text in Research Archive
• Agram, Nacira & Øksendal, Bernt Karsten (2023). Stochastic Fokker–Planck Equations for Conditional McKean–Vlasov Jump Diffusions and Applications to Optimal Control. SIAM Journal of Control and Optimization. ISSN 0363-0129. 61(3), p. 1472–1493. doi: 10.1137/21M1461034. Full text in Research Archive
• Benth, Fred Espen & Karbach, Sven (2023). Multivariate continuous-time autoregressive moving-average processes on cones. Stochastic Processes and their Applications. ISSN 0304-4149. 162, p. 299–337. doi: 10.1016/j.spa.2023.05.003.
• Moulay Hachemi, Rahma Yasmina & Øksendal, Bernt Karsten (2023). The fractional stochastic heat equation driven by time-space white noise. Fractional Calculus and Applied Analysis. ISSN 1311-0454. 26(2), p. 513–532. doi: 10.1007/s13540-023-00134-7. Full text in Research Archive
• Puica, Mihaela-Alexandra; Dehant, V.; Folgueira, M.; Van Hoolst, Hoolst & Rekier, J. (2023). Analytical computation of total topographic torque at the core-mantle boundary and its impact on tidally driven length-of-day variations. Geophysical Journal International. ISSN 0956-540X. 234(1), p. 585–596. doi: 10.1093/gji/ggad077. Full text in Research Archive
• Di Nunno, Giulia & Giordano, Michele (2023). Stochastic Volterra equations with time-changed Lévy noise and maximum principles. Annals of Operations Research. ISSN 0254-5330. doi: 10.1007/s10479-023-05303-8. Full text in Research Archive Show summary

  Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed Lévy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative introduced in Di Nunno and Eide (Stoch Anal Appl 28:54-85, 2009). We prove both a sufficient and necessary stochastic maximum principle.

• Agrell, Christian; Dahl, Kristina Rognlien & Hafver, Andreas (2023). Optimal sequential decision making with probabilistic digital twins. SN Applied Sciences. ISSN 2523-3963. 5(4). doi: 10.1007/s42452-023-05316-9. Full text in Research Archive Show summary

  In this study, we present a formal defnition of the probabilistic digital twin (PDT). Digital twins are emerging in many industries, typically consisting of simulation models and data associated with a specifc physical system. In order to defne probabilistic digital twins, we discuss how epistemic uncertainty can be treated using measure theory, by modelling epistemic information via sigma-algebras. A gentle introduction to the necessary mathematical theory is provided throughout the paper, together with a number of examples to illustrate the core concepts. We then introduce the problem of optimal sequential decision making. That is, when the outcome of each decision may inform the next. We discuss how this problem may be solved theoretically, and the current limitations that prohibit most practical applications. As a numerically tractable alternative, we propose a generic approximate solution using deep reinforcement learning together with neural networks defined on sets. We illustrate the method on a practical problem, considering optimal information gathering for the estimation of a failure probability.

• Lindstrøm, Tom Louis (2023). The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis. In Hilbert, Astrid; Mastrogiacomo, Elisa; Mazzucchi, Sonia; Rüdiger, Barbara & Ugolini, Stefania (Ed.), Quantum and Stochastic Mathematical Physics. Springer. ISSN 978-3-031-14031-0. p. 187–215. doi: 10.1007/978-3-031-14031-0_9. Full text in Research Archive
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2023). Well-posedness of the deterministic transport equation with singular velocity field perturbed along fractional Brownian paths. Journal of Differential Equations. ISSN 0022-0396. 362, p. 106–172. doi: 10.1016/j.jde.2023.02.059. Full text in Research Archive
• Miao, Yingting; Rohde, Christian & Tang, Hao (2023). Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. doi: 10.1007/s40072-023-00291-z. Full text in Research Archive
• Di Nunno, Giulia; Ortiz-Latorre, Salvador & Petersson, Andreas Erik (2023). SPDE bridges with observation noise and their spatial approximation. Stochastic Processes and their Applications. ISSN 0304-4149. 158, p. 170–207. doi: 10.1016/j.spa.2023.01.007. Full text in Research Archive
• Dordevic, Jasmina & Jovanović, Bojana (2023). Dynamical analysis of a stochastic delayed epidemic model with lévy jumps and regime switching. Journal of the Franklin Institute. ISSN 0016-0032. 360(2), p. 1252–1283. doi: 10.1016/j.jfranklin.2022.12.009. Full text in Research Archive
• Baños, David; Bauer, Martin; Meyer-Brandis, Thilo & Proske, Frank Norbert (2023). Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise. Potential Analysis. ISSN 0926-2601. doi: 10.1007/s11118-023-10069-6. Full text in Research Archive
• Larsson, Karl; Green, Rikard & Benth, Fred Espen (2023). A stochastic time-series model for solar irradiation. Energy Economics. ISSN 0140-9883. 117. doi: 10.1016/j.eneco.2022.106421. Full text in Research Archive
• Tang, Hao & Yang, Anita (2023). Noise effects in some stochastic evolution equations: Global existence and dependence on initial data. Annales de l'I.H.P. Probabilites et statistiques. ISSN 0246-0203. 59(1), p. 378–410. doi: 10.1214/21-AIHP1241. Full text in Research Archive
• Tang, Hao & Wang, Zhi-An (2023). Strong solutions to a nonlinear stochastic aggregation-diffusion equation. Communications in Contemporary Mathematics. ISSN 0219-1997. doi: 10.1142/S0219199722500730.
• Grochowicz, Aleksander; van Greevenbroek, Koen; Benth, Fred Espen & Zeyringer, Marianne (2023). Intersecting near-optimal spaces: European power systems with more resilience to weather variability. Energy Economics. ISSN 0140-9883. 118. doi: 10.1016/j.eneco.2022.106496. Full text in Research Archive Show summary

  We suggest a new methodology for designing robust energy systems. For this, we investigate so-called near-optimal solutions to energy system optimisation models; solutions whose objective values deviate only marginally from the optimum. Using a refined method for obtaining explicit geometric descriptions of these near-optimal feasible spaces, we find designs that are as robust as possible to perturbations. This contributes to the ongoing debate on how to define and work with robustness in energy systems modelling. We apply our methods in an investigation using multiple decades of weather data. For the first time, we run a capacity expansion model of the European power system (one node per country) with a three-hourly temporal resolution and 41 years of weather data. While an optimisation with 41 weather years is at the limits of computational feasibility, we use the near-optimal feasible spaces of single years to gain an understanding of the design space over the full time period. Specifically, we intersect all near-optimal feasible spaces for the individual years in order to get designs that are likely to be feasible over the entire time period. We find significant potential for investment flexibility, and verify the feasibility of these designs by simulating the resulting dispatch problem with four decades of weather data. They are characterised by a shift towards more onshore wind and solar power, while emitting more than 50% less CO2 than a cost-optimal solution over that period. Our work builds on recent developments in the field, including techniques such as Modelling to Generate Alternatives (MGA) and Modelling All Alternatives (MAA), and provides new insights into the geometry of near-optimal feasible spaces and the importance of multi-decade weather variability for energy systems design. We also provide an effective way of working with a multi-decade time frame in a highly parallelised manner. Our implementation is open-sourced, adaptable and is based on PyPSA-Eur.

• Lindstrøm, Tom Louis & Ross, David Andrew (2023). A nonstandard approach to asymptotic fixed point theorems. Journal of Fixed Point Theory and Applications. ISSN 1661-7738. 25(1). doi: 10.1007/s11784-022-01028-6. Full text in Research Archive Show summary

  We use methods from nonstandard analysis to unify and extend results from the theory of asymptotic fixed points on metric spaces. Among the topics we consider are Kirk’s asymptotic fixed point theorem with extensions, Boyd and Wong’s fixed point theorem, and Suzuki’s fixed point theorem for asymptotic contractions of the Meier–Keeler type. We also show how Suzuki’s asymptotic contractions of the final type can be modified to yield uniform convergence on compact and bounded sets.

• Kersting, Hans; Orvieto, Antonio; Proske, Frank Norbert & Lucchi, Aurelien (2023). Mean first exit times of Ornstein-Uhlenbeck processes in high-dimensional spaces. Journal of Physics A: Mathematical and Theoretical. ISSN 1751-8113. 56(21). doi: 10.1088/1751-8121/acc559. Full text in Research Archive
• Di Nunno, Giulia; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2023). Sandwiched SDEs with unbounded drift driven by Hölder noises. Advances in Applied Probability. ISSN 0001-8678. 55(3), p. 927–964. doi: 10.1017/apr.2022.56. Full text in Research Archive
• Aman, Auguste; Coulibaly, Harouna & Dordevic, Jasmina (2023). Forward-backward stochastic differential equations with delay generators. Stochastics and Dynamics. ISSN 0219-4937. 23(02). doi: 10.1142/S0219493723500120. Full text in Research Archive
• Savku, Emel (2022). Fundamentals of Market Making Via Stochastic Optimal Control. In Purutçuoğlu, Vilda; Weber, Gerhard-Wilhelm & Farnoudkia, Hajar (Ed.), Operations Research: New Paradigms and Emerging Applications. CRC Press. ISSN 978-1-032-34926-8. p. 136–154.
• Dahl, Kristina Rognlien; Huseby, Arne Bang & Havgar, Marius (2022). Optimal Reinsurance Contracts under Conditional Value-at-risk. In Leva, Maria Chiara; Patelli, Edoardo; Podofillini, Luca & Wilson, Simon (Ed.), Proceedings of the 32nd European Safety and Reliability Conference (ESREL 2022). Research Publishing Services. ISSN 978-981-18-5183-4. Show summary

  An insurance contract implies that risk is ceded from ordinary policy holders to companies. However, companies do the same thing between themselves, and this is known as reinsurance. The problem of determining reinsurance contracts which are optimal with respect to some reasonable criterion has been studied extensively within actuarial science. Different contract types are considered such as stop-loss contracts where the reinsurance company covers risk above a certain level, and insurance layer contracts where the reinsurance company covers risk within an interval. The contracts are then optimized with respect to some risk measure, such as value-at-risk or conditional value-at- risk. In the present paper we consider the problem of minimizing conditional value-at-risk in the case of multiple stop-loss contracts. Such contracts are known to be optimal in the univariate case, and the optimal contract is easily determined. We show that the same holds in the multivariate case, both with dependent and independent risks. The results are illustrated with some numerical examples.

• Huseby, Arne Bang (2022). Optimizing Multiple Reinsurance Contracts. In Leva, Maria Chiara; Patelli, Edoardo; Podofillini, Luca & Wilson, Simon (Ed.), Proceedings of the 32nd European Safety and Reliability Conference (ESREL 2022). Research Publishing Services. ISSN 978-981-18-5183-4. Show summary

  An insurance contract implies that risk is ceded from ordinary policy holders to companies. Companies do the same thing between themselves, and this is known as reinsurance. The problem of determining reinsurance contracts which are optimal with respect to some reasonable criterion has been studied extensively. Different contract types are considered such as stop-loss contracts where the reinsurance company covers risk above a certain level, and insurance layer contracts where the reinsurance company covers risk within an interval. The contracts are then optimized with respect to some risk measure, such as value-at-risk or conditional tail expectation. In the present paper we investigate this problem further and show that the optimal solution depends on the tail hazard rates of the risk distributions. If the tail hazard rates are decreasing, which is the case for heavy tailed distributions like lognormal and pareto distributions, the optimal solution is balanced. That is, reinsurance contracts for identically distributed risks should be identical insurance layer contracts. However, if the tail hazard rate is increasing, which is the case for light tailed distributions like truncated normal distributions, the optimal solution is typically not balanced. Even for identically distributed risks, some contracts should be insurance layer contracts, while others should be stop-loss contracts. In the limiting case, where the hazard rate is constant, i.e., when the risks are exponentially distributed, we show that a balanced solution is optimal. We also present an efficient importance sampling method for estimating optimal contracts.

• Bogso, Antoine-Marie; Dieye, Moustapha; Menoukeu-Pamen, Olivier & Proske, Frank Norbert (2022). SMOOTHNESS OF SOLUTIONS OF HYPERBOLIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH L∞-VECTOR FIELDS. arXiv.org. ISSN 2331-8422.
• Benth, Fred Espen; Detering, Nils & Galimberti, Luca (2022). Neural networks in Fréchet spaces. Annals of Mathematics and Artificial Intelligence. ISSN 1012-2443. 91, p. 75–103. doi: 10.1007/s10472-022-09824-z. Full text in Research Archive
• Coffie, Emmanuel; Mao, Xuerong & Proske, Frank Norbert (2022). On the Analysis of a Generalised Rough Ait-Sahalia Interest Rate Model. arXiv.org. ISSN 2331-8422.
• Kalinin, Alexander; Meyer-Brandis, Thilo & Proske, Frank Norbert (2022). Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments. arXiv.org. ISSN 2331-8422.
• Orvieto, Antonio; Kersting, Hans; Proske, Frank Norbert; Bach, Francis & Lucchi, Aurelien (2022). Anticorrelated Noise Injection for Improved Generalization. Proceedings of Machine Learning Research (PMLR). ISSN 2640-3498. 162, p. 17094–17116. Full text in Research Archive
• Lucchi, Aurelien; Proske, Frank Norbert; Orvieto, Antonio; Bach, Francis & Kersting, Hans (2022). On the Theoretical Properties of Noise Correlation in Stochastic Optimization. Advances in Neural Information Processing Systems. ISSN 1049-5258. Full text in Research Archive
• Coffie, Emmanuel; Duedahl, Sindre & Proske, Frank Norbert (2022). Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut-Elworthy-Li formula for singular SDEs. Stochastic Processes and their Applications. ISSN 0304-4149. 156, p. 156–195. doi: 10.1016/j.spa.2022.11.001. Full text in Research Archive
• Crisan, Dan; Lobbe, Alexander & Ortiz-Latorre, Salvador (2022). Pathwise Approximations for the Solution of the Non-Linear Filtering Problem. In Yin, George & Zariphopoulou, Thaleia (Ed.), Stochastic Analysis, Filtering, and Stochastic Optimization - A Commemorative Volume to Honor Mark H. A. Davis’s Contributions. Springer Nature. ISSN 978-3-030-98518-9. p. 79–99. doi: 10.1007/978-3-030-98519-6_4.
• Kovács, Mihály; Lang, Annika & Petersson, Andreas Erik (2022). Approximation of SPDE covariance operators by finite elements: a semigroup approach. IMA Journal of Numerical Analysis. ISSN 0272-4979. 43(3), p. 1324–1357. doi: 10.1093/imanum/drac020. Full text in Research Archive
• Di Nunno, Giulia; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2022). Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises. Numerical Algorithms. ISSN 1017-1398. doi: 10.1007/s11075-022-01424-6. Full text in Research Archive
• Crisan, Dan; Lobbe, Alexander & Ortiz-Latorre, Salvador (2022). An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. 10, p. 1050–1081. doi: 10.1007/s40072-022-00260-y. Full text in Research Archive
• Dordevic, Jasmina (2022). A stochastic model for malaria and its behavior under insecticide-treated nets. Studies in applied mathematics (Cambridge). ISSN 0022-2526. 149(3), p. 631–656. doi: 10.1111/sapm.12515. Full text in Research Archive
• Schrader, Simon Elias & Benth, Fred Espen (2022). A stochastic study of carbon emission reduction from electrification and interconnecting cable utilization. The Norway and Germany case. Energy Economics. ISSN 0140-9883. 114. doi: 10.1016/j.eneco.2022.106300. Full text in Research Archive
• Di Nunno, Giulia (2022). On stochastic control for time changed Lévy dynamics. SeMA Journal - Boletin de la Sociedad Española de Matemática Aplicada. ISSN 2254-3902. 79, p. 529–547. doi: 10.1007/s40324-022-00301-5. Full text in Research Archive Show summary

  Controlled stochastic differential equations driven by time changed Lévy noises do not enjoy the Markov property in general, but can be treated in the framework of general martingales. From the modelling point of view, time changed noises constitute a feasible way to include time dependencies at noise level and still keep a reasonably simple structure. Furthermore, they are easy to simulate, with the result that time change Lévy dynamics attract attention in various fields of application. In this work we survey an approach to stochastic control via maximum principle for time changed Lévy dynamics. We emphasise the role and use of different information flows in tackling the various control problems. We show how these techniques can be extended to include Volterra type dynamics and the control of forward–backward systems of equations. Our techniques make use of the stochastic non-anticipating (NA) derivative in a general martingale framework.

• Alonso-Orán, Diego; Miao, Yingting & Tang, Hao (2022). Global existence, blow-up and stability for a stochastic transport equation with non-local velocity. Journal of Differential Equations. ISSN 0022-0396. 335, p. 244–293. doi: 10.1016/j.jde.2022.06.025. Full text in Research Archive
• Kovács, Mihály; Lang, Annika & Petersson, Andreas Erik (2022). Hilbert–Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations. Stochastic Analysis and Applications. ISSN 0736-2994. doi: 10.1080/07362994.2022.2053541. Full text in Research Archive
• Midtfjord, Alise Danielle; De Bin, Riccardo & Huseby, Arne Bang (2022). A boosting model for survival analysis with dependent censoring. In Torelli, Nicola; BELLIO, RUGGERO & MUGGEO, VITO (Ed.), Proceedings of the 36th International Workshop on Statistical Modelling. EUT Edizioni Università di Trieste. ISSN 978-88-5511-309-0.
• Dordevic, Jasmina & Dahl, Kristina Rognlien (2022). Stochastic optimal control of pre-exposure prophylaxis for HIV infection. Mathematical Medicine and Biology. ISSN 1477-8599. 39(3), p. 197–225. doi: 10.1093/imammb/dqac003.
• Galeati, Lucio; Harang, Fabian Andsem & Mayorcas, Avi (2022). Distribution dependent SDEs driven by additive fractional Brownian motion. Probability theory and related fields. ISSN 0178-8051. p. 1–59. doi: 10.1007/s00440-022-01145-w. Full text in Research Archive
• Harang, Fabian Andsem; Tindel, Samy & Wang, Xiaohua (2022). Volterra equations driven by rough signals 2: higher order expansions. Stochastics and Dynamics. ISSN 0219-4937. doi: 10.1142/S0219493723500028. Full text in Research Archive
• Midtfjord, Alise Danielle; De Bin, Riccardo & Huseby, Arne Bang (2022). A decision support system for safer airplane landings: Predicting runway conditions using XGBoost and explainable AI. Cold Regions Science and Technology. ISSN 0165-232X. 199. doi: 10.1016/j.coldregions.2022.103556. Full text in Research Archive
• Craig, Michael T.; Wohland, Jan; Stoop, Laurens P.; Kies, Alexander; Pickering, Bryn & Bloomfield, Hannah C. [Show all 23 contributors for this article] (2022). Overcoming the disconnect between energy system and climate modeling. Joule. ISSN 2542-4351. 6(7), p. 1405–1417. doi: 10.1016/j.joule.2022.05.010. Full text in Research Archive Show summary

  Energy system models underpin decisions by energy system planners and operators. Energy system modeling faces a transformation: accounting for changing meteorological conditions imposed by climate change. To enable that transformation, a community of practice in energy-climate modeling has started to form that aims to better integrate energy system models with weather and climate models. Here, we evaluate the disconnects between the energy system and climate modeling communities, then lay out a research agenda to bridge those disconnects. In the near-term, we propose interdisciplinary activities for expediting uptake of future climate data in energy system modeling. In the long-term, we propose a transdisciplinary approach to enable development of (1) energy-system-tailored climate datasets for historical and future meteorological conditions and (2) energy system models that can effectively leverage those datasets. This agenda increases the odds of meeting ambitious climate mitigation goals by systematically capturing and mitigating climate risk in energy sector decision-making.

• Dahl, Kristina Rognlien & Eyjolfsson, Heidar (2022). Self-exciting jump processes and their asymptotic behaviour. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2022.2028789. Full text in Research Archive
• Benth, Fred Espen & Galimberti, Luca (2022). Stochastic integrals and Gelfand integration in Fréchet spaces. Infinite Dimensional Analysis Quantum Probability and Related Topics. ISSN 0219-0257. 25(2), p. 1–35. doi: 10.1142/S0219025722500072. Full text in Research Archive
• Benth, Fred Espen; Detering, Nils & Krühner, Paul (2022). Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. p. 1–23. doi: 10.1080/17442508.2021.2019738. Full text in Research Archive
• Agram, Nacira; Labed, Saloua; Øksendal, Bernt Karsten & Yakhlef, Samia (2022). Singular Control of Stochastic Volterra Integral Equations. Acta Mathematica Scientia. ISSN 0252-9602. 42(3), p. 1003–1017. doi: 10.1007/s10473-022-0311-9. Full text in Research Archive
• Benth, Fred Espen; Nunno, Giulia Di & Schroers, Dennis (2022). A topological proof of Sklar's theorem in arbitrary dimensions. Dependence Modeling. ISSN 2300-2298. 10(1), p. 22–28. doi: 10.1515/demo-2022-0103. Full text in Research Archive
• Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2022). Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2022.2047188. Full text in Research Archive
• Agram, Nacira; Hu, Yaozhong & Øksendal, Bernt Karsten (2022). Mean-field backward stochastic differential equations and applications. Systems & control letters (Print). ISSN 0167-6911. 162. doi: 10.1016/j.sysconle.2022.105196. Full text in Research Archive
• Galeati, Lucio; Harang, Fabian Andsem & Mayorcas, Avi (2022). Distribution dependent SDEs driven by additive continuous noise. Electronic Journal of Probability (EJP). ISSN 1083-6489. 27, p. 1–38. doi: 10.1214/22-EJP756. Full text in Research Archive
• Benth, Fred Espen; Schroers, Dennis & Veraart, Almut E. D. (2022). A weak law of large numbers for realised covariation in a Hilbert space setting. Stochastic Processes and their Applications. ISSN 0304-4149. 145, p. 241–268. doi: 10.1016/j.spa.2021.12.011. Full text in Research Archive
• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2022). Stochastic Modeling of Stratospheric Temperature. Mathematical Geosciences. ISSN 1874-8961. 54, p. 651–678. doi: 10.1007/s11004-021-09990-6. Full text in Research Archive Show summary

  This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

• Harang, Fabian Andsem; Nilssen, Torstein & Proske, Frank Norbert (2022). GIRSANOV THEOREM FOR MULTIFRACTIONAL BROWNIAN PROCESSES. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2022.2027948. Full text in Research Archive
• Galeati, Lucio & Harang, Fabian Andsem (2022). Regularization of multiplicative SDEs through additive noise. The Annals of Applied Probability. ISSN 1050-5164. 32(5), p. 3930–3963. doi: 10.1214/21-AAP1778. Full text in Research Archive
• Dahl, Kristina Rognlien & Eyjolfsson, Heidar (2021). Self-Exciting Jump Processes as Deterioration Models. In Castanier, Bruno; Cepin, Marko; Bigaud, David & Berenguer, Christophe (Ed.), Proceedings of the 31st European Safety and Reliability Conference. Research Publishing Services. ISSN 978-981-18-2016-8. doi: 10.3850/978-981-18-2016-8_286-cd. Full text in Research Archive
• Pilipenko, Andrey & Proske, Frank Norbert (2021). Small Noise Perturbations in Multidimensional Case. arXiv.org. ISSN 2331-8422.
• Coffie, Emmanuel; Duedahl, Sindre & Proske, Frank Norbert (2021). Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs. arXiv.org. ISSN 2331-8422.
• Coffie, Emmanuel; Duedahl, Sindre & Proske, Frank Norbert (2021). Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space. arXiv.org. ISSN 2331-8422.
• Kalinin, Alexander; Meyer-Brandis, Thilo & Proske, Frank Norbert (2021). Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach. arXiv.org. ISSN 2331-8422.
• Crisan, Dan; Kurtz, Thomas G. & Ortiz-Latorre, Salvador (2021). Particle Representation for the Solution of the Filtering Problem. Application to the Error Expansion of Filtering Discretizations. Journal of Stochastic Analysis (JOSA). ISSN 2689-6931. doi: 10.31390/josa.2.3.15. Full text in Research Archive Show summary

  We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In this paper, we explore some of its theoretical con- sequences. The first is to deduce the equations satisfied by the solution of the filtering problem in three different frameworks: the signal independent Brownian measurement noise model, the spatial observations with additive white noise model and the cluster detection model in spatial point processes. Secondly we use the representation to show that a suitably chosen filtering discretisation converges to the filtering solution. Thirdly we study the leading error coefficient for the discretisation. We show that it satisfies a stochastic partial differential equation by exploiting the weighted particle representation for both the approximation and the limiting filtering solution.

• Midtfjord, Alise Danielle; De Bin, Riccardo & Huseby, Arne Bang (2021). A Machine Learning Approach to Safer Airplane Landings: Predicting Runway Conditions using Weather and Flight Data. arXiv.org. ISSN 2331-8422. Show summary

  The presence of snow and ice on runway surfaces reduces the available tire-pavement friction needed for retardation and directional control and causes potential economic and safety threats for the aviation industry. To activate appropriate safety procedures, pilots need accurate and timely information on the actual runway surface conditions. In this study, XGBoost is used to create a combined runway assessment system, which includes a classification model to identify slippery conditions and a regression model to predict the level of slipperiness. The models are trained on weather data and runway reports. The runway surface conditions are represented by the tire-pavement friction coefficient, which is estimated from flight sensor data from landing aircrafts. The XGBoost models are combined with SHAP approximations to provide a reliable decision support system for airport operators and pilots, which can contribute to safer and more economic operations of airport runways. To evaluate the performance of the prediction models, they are compared to several state-of-the-art runway assessment methods. The XGBoost models identify slippery runway conditions with a ROC AUC of 0.95, predict the friction coefficient with a MAE of 0.0254, and outperforms all the previous methods. The results show the strong abilities of machine learning methods to model complex, physical phenomena with a good accuracy.

• Benth, Fred Espen & Simonsen, Iben Cathrine (2021). Metatimes, random measures and cylindrical random variables. Modern Stochastics: Theory and Applications (MSTA). ISSN 2351-6046. 8(3), p. 349–371. doi: 10.15559/21-VMSTA178. Full text in Research Archive
• Harang, Fabian Andsem & Catellier, Rémi (2021). Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation. arXiv.org. ISSN 2331-8422.
• Harang, Fabian Andsem & Mayorcas, Avi (2020). Pathwise regularisation of singular interacting particle systems and their mean field limits. Stochastic Processes and their Applications. ISSN 0304-4149. 159, p. 499–540. doi: 10.1016/j.spa.2023.02.005.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2020). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths. arXiv.org. ISSN 2331-8422.
• Vanem, Erik & Huseby, Arne (2019). Environmental Contours for Safe Design of Ships and Other Marine Structures, Book of Proceedings. 2nd International Conference on Structural Integrity for Offshore Energy Industry. ASRANET. ISSN 978-1-9996144-3-0. p. 70–77.
• Baños, David; Bauer, Martin; Meyer-Brandis, Thilo & Proske, Frank Norbert (2019). Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise. arXiv.org. ISSN 2331-8422. Full text in Research Archive
• Agram, Nacira; Haadem, Sven; Øksendal, Bernt & Proske, Frank Norbert (2018). Optimal stopping, randomized stopping and singular control with partial information flow. arXiv.org. ISSN 2331-8422.
• Amine, Oussama; Banos, David & Proske, Frank Norbert (2018). Regularity Properties of the Stochastic Flow of a Skew Fractional Brownian Motion. arXiv.org. ISSN 2331-8422. doi: 10.1142/s0219025720500058.
• Amine, Oussama; Coffie, Emmanuel; Harang, Fabian Andsem & Proske, Frank Norbert (2018). A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling. arXiv.org. ISSN 2331-8422.
• Vanem, Erik & Huseby, Arne (2018). Seasonal and Omni-Seasonal Environmental Contours for Extreme Sea States, Proceedings of the 7th International Maritime Conference on Design for Safety, DfS 2018. Osaka University. ISSN 978-4-908678-12-7. p. 148–159.
• Agram, Nacira; Hilbert, Astrid & Øksendal, Bernt (2018). SPDEs with Space-Mean Dynamics. arXiv.org. ISSN 2331-8422. doi: 10.3934/mcrf.2020004.
• Agram, Nacira & Øksendal, Bernt (2018). Mean-Field Stochastic Control with Elephant Memory in Finite and Infinite Time Horizon. arXiv.org. ISSN 2331-8422. doi: 10.1080/17442508.2019.1635600.
• Agram, Nacira; Labed, Saloua & Mansouri, Badreddine (2018). Reflected Advanced Backward Stochastic Differential Equations with Default. arXiv.org. ISSN 2331-8422.
• Agram, Nacira (2018). Dynamic risk measure for BSVIE with jumps and semimartingale issues. arXiv.org. ISSN 2331-8422. doi: 10.1080/07362994.2019.1569531.

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• Benth, Fred Espen & Krühner, Paul (2023). Stochastic Models for Prices Dynamics in Energy and Commodity Markets An Infinite-Dimensional Perspective. Springer. ISBN 978-3-031-40366-8. 250 p.
• Barndorff-Nielsen, Ole E.; Benth, Fred Espen & Veraart, Almut E. D. (2018). Ambit Stochastics. Springer Nature. ISBN 978-3-319-94128-8. 402 p.
• Celledoni, Elena; Di Nunno, Giulia; Ebrahimi-Fard, Kurusch & Munthe-Kaas, Hans (2018). Computation and Combinatorics in Dynamics, Stochastics and Control. Springer. ISBN 978-3-030-01592-3. 13(1). 737 p. Show summary

  The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

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• Viole, Isabelle; van Greevenbroek, Koen & Cheng, Claudia Siew Wan (2024). Can Norway save the European Union's hydrogen ambition for 2030?
• Lindstrøm, Tom Louis (2024). Historien om å løse ligninger.
• Yurchenko-Tytarenko, Anton (2024). Quadratic hedging in SVV-model.
• Zamora Font, Oriol; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes stochastic volatility model: Change of measure and Thiele's PIDE.
• Ortiz-Latorre, Salvador (2023). Strong solutions for singular SDEs driven by fractional Brownian motion.
• Huseby, Arne Bang (2023). Domination and multistate systems. Show summary

  Domination theory has been studied extensively in the context of binary monotone systems, where the structure function is a sum of products of the component states, and with coefficients given by the signed domination function. Using e.g., matroid theory, many useful properties of the signed domination function can be derived. In this paper we show how some of these results can be extended to multistate systems. The signed domination function is an invariant determined by the poset generated by the minimal path vectors. Two systems with isomorphic posets also have the same signed domination function. We derive an explicit formula for the domination using Möbius functions. Furthermore, we obtain a recursive formula for the signed domination function, referred to as the signed domination theorem. Both these results are generalizations of the corresponding results for binary monotone systems.

• Grochowicz, Aleksander (2023). Spatio-temporal smoothing and dynamics of different electricity flexibility options.
• Grochowicz, Aleksander (2023). Identifying weather stress events from power system optimisation outputs.
• Grochowicz, Aleksander; Greevenbroek, Koen van & Bloomfield, Hannah C. (2023). Identifying weather stress events from power system optimisation outputs.
• Petersson, Andreas Erik (2023). Noise Simulation in Finite Element Methods for SPDE Approximation.
• Petersson, Andreas Erik (2023). Piecewise linear interpolation of noise in finite element approximations of parabolic SPDEs.
• Petersson, Andreas Erik (2023). SPDE bridges with observation noise and their spatial approximation.
• Petersson, Andreas Erik (2023). The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation.
• Savku, Emel (2023). A Nonzero-Sum Regime-Switching Stochastic Differential Game Application with Constraints.
• Di Nunno, Giulia (2023). On stochastic control for time changed Lévy dynamics.
• Di Nunno, Giulia (2023). Horizon risk and fully dynamic risk measures.
• Di Nunno, Giulia (2023). Pricing in sandwiched Volterra volatility models.
• Di Nunno, Giulia (2023). Dynamic risk assessment, horizon risk, and interest rate uncertainty.
• Di Nunno, Giulia (2023). Sandwiched Volterra volatility models and hedging.
• Di Nunno, Giulia (2023). Sandwiched Volterra volatility models and hedging.
• Di Nunno, Giulia (2023). Sandwiched Volterra volatility models and hedging.
• Di Nunno, Giulia (2023). Optimal control for Volterra type dynamics.
• Di Nunno, Giulia (2023). Sandwiched Volterra volatility models and option pricing.
• Di Nunno, Giulia (2023). Lifting of Volterra processes: Optimal control in UMD Banach spaces .
• Di Nunno, Giulia (2023). Research on Risk Measures.
• Di Nunno, Giulia (2023). Horizon risk and dynamic risk assessment.
• Di Nunno, Giulia (2023). Horizon risk and fully dynamic risk measures.
• Ortiz-Latorre, Salvador (2023). Time discretizations for the nonlinear filtering problem.
• Ortiz-Latorre, Salvador (2023). Robust discretizations for the solution of the non-linear filtering problem.
• Ortiz-Latorre, Salvador (2023). SPDE bridges with observation noise and their spatial approximation.
• Ortiz-Latorre, Salvador (2023). Robust approximations for the solution of the non-linear filtering problem.
• Ortiz-Latorre, Salvador (2023). Strong solutions for singular SDEs driven by fractional Brownian motion.
• Yurchenko-Tytarenko, Anton (2023). Volterra sandwiched volatility model: Markovian approximation and hedging.
• Yurchenko-Tytarenko, Anton (2023). CIR process and Skorokhod problems]{Cox-Ingersoll-Ross process and Skorokhod problems.
• Yurchenko-Tytarenko, Anton (2023). Volterra sandwiched volatility model: Markovian approximation and hedging.
• Yurchenko-Tytarenko, Anton (2023). Volterra sandwiched volatility model: Markovian approximation and hedging.
• Yurchenko-Tytarenko, Anton (2023). Hedging in Volterra volatility models.
• Yurchenko-Tytarenko, Anton (2023). Parameter estimation in rough Bessel model.
• Yurchenko-Tytarenko, Anton (2023). Power law in SVV model.
• Diaz Lozano, Pere (2023). Neural SDEs for Conditional Time Series Generation using the Signature Wasserstein-1 metric.
• Grochowicz, Aleksander (2023). The role of historical weather data and how that can be used for a more resilient energy transition.
• Grochowicz, Aleksander; van Greevenbroek, Koen; Benth, Fred Espen & Zeyringer, Marianne (2023). Intersecting Near-Optimal Spaces for Policy Information.
• van Greevenbroek, Koen; Grochowicz, Aleksander & Bloomfield, Hannah C. (2023). Identifying Weather Stress Events from Power System Optimisation Outputs.
• Zamora Font, Oriol; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes Stochastic Volatility Model: Change of Measure and Forward Variance.
• Zamora Font, Oriol; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes stochastic volatility model: change of measure and forward variance.
• Greevenbroek, Koen van; Grochowicz, Aleksander; Zeyringer, Marianne; Noll, Josef & Vågerö, Oskar (2023). Vi treng uavhengig forsking, ikkje drøymetenking om kjernekraft. Aftenposten (morgenutg. : trykt utg.). ISSN 0804-3116.
• Grochowicz, Aleksander & Zeyringer, Marianne (2023). Managing the variability in time and space of renewable power generation.
• Grochowicz, Aleksander & Zeyringer, Marianne (2023). Managing the variability in time and geography of renewable power generation.
• Eggen, Mari Dahl; Midtfjord, Alise Danielle; Vorobeva, Ekaterina; Benth, Fred Espen; Hupe, Patrick & Brissaud, Quentin [Show all 10 contributors for this article] (2023). Using a machine learning and stochastics-founded model to provide near real-time stratospheric polar vortex diagnostics based on high-latitude infrasound data. Show summary

  Acoustic waves below the frequency limit of human hearing - infrasound - can travel for thousands of kilometres in the atmosphere. The global propagation signature of infrasound is highly sensitive to the wind structure of the stratosphere. This work exploits processed continuous data from three high-latitude infrasound stations to characterize an aspect of the stratospheric polar vortex. Concretely, a mapping is developed which takes the infrasound data from these three stations as input and outputs an estimate of the polar cap zonal mean wind averaged over 60-90 degrees in latitude at the 1 hPa pressure level. This stratospheric diagnostic information is relevant to, for example, sudden stratospheric warming assessment and sub-seasonal prediction. The considered acoustic data is within a low-frequency regime globally dominated by so-called microbarom infrasound, which is continuously radiated into the atmosphere due to nonlinear interaction between counter-propagating ocean surface waves. We trained a stochastics-based machine learning model (delay-SDE-net) to map between a time series of five years (2014-2018) of processed infrasound data and the ERA5 (reanalysis-based) daily average polar cap wind at 1 hPa for the same period. The ERA5 data was hence treated as ground-truth. In the prediction, the delay-SDE-net utilizes time-lagged inputs and their dependencies, as well as the day of the year to account for seasonal differences. In the validation phase, the input was the 2019 and 2020 infrasound time series, and the model inference results in an estimate of the daily average polar cap wind time-series. This result was then compared to the ERA5 representation of the stratospheric diagnostic time-series for the same period. The applied machine learning model is based on stochastics and allows for an interpretable approach to estimate the aleatoric and epistemic prediction uncertainties. It is found that the mapping, which is only informed of the trained model, the day of year, and the infrasound data from three stations, generates a 1 hPa polar cap average wind estimate with a prediction error standard deviation of around 10 m/s compared to ERA5. Focus should be put on the winter months because this is when the coupling between the stratosphere and the troposphere can mostly influence the surface conditions and provide additional prediction skill, in particular during strong and weak stratospheric polar vortex regimes. The infrasound data is available in real-time, and we discuss how the developed approach can be extended to provide near real-time stratospheric polar vortex diagnostics.

• Savku, Emel (2023). A Stochastic Maximum Principle Approach for a Nash Equilibrium of a Nonzero-Sum Game.
• Savku, Emel (2023). Stochastic Maximum Principle For A Constraint Nonzero-Sum Game Application:Bancassurance.
• van Greevenbroek, Koen; Zeyringer, Marianne; Noll, Josef; Grochowicz, Aleksander & Vågerö, Oskar (2023). Kjernekraft er ikkje naudsynt for Noreg. Det vil heller ikkje lønna seg. Aftenposten (morgenutg. : trykt utg.). ISSN 0804-3116.
• Melteig, Elina & Grochowicz, Aleksander (2023). Strømmarkedet: Hva skjer hvis vi kobler Nord- og Sør-Norge? . [Internet]. forskning.no, tu.no, titan.uio.no.
• Ortiz-Latorre, Salvador (2023). Pathwise approximations for the solution of the non-linear filtering problem.
• Ortiz-Latorre, Salvador (2022). Deep learning methods for the stochastic filtering problem.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2022). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2022). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Benth, Fred Espen (2022). Klima og vær - data og risiko.
• Yurchenko-Tytarenko, Anton (2022). Volterra Sandwiched Volatility models.
• Yurchenko-Tytarenko, Anton (2022). Volterra sandwiched volatility model: Markovian approximation and hedging.
• Yurchenko-Tytarenko, Anton (2022). Volterra Sandwiched Volatility models.
• Di Nunno, Giulia; Natalini, Roberto & Luca, Perri (2022). La matematica unisce. [Internet]. https://www.youtube.com/watch?v=-Sj-3w0GXvw.
• Di Nunno, Giulia (2022). Fully-dynamic risk measures and horizon risk.
• Di Nunno, Giulia (2022). Stochastic games for Volterra time-changed Lévy dynamics.
• Di Nunno, Giulia (2022). On time changed Lévy noises in modelling, dynamics and control .
• Di Nunno, Giulia (2022). Stochastic games for Volterra time-changed Lévy dynamics.
• Di Nunno, Giulia (2022). Sandwiched SDEs with unbounded drift, Hölder noises and stochastic volatility modelling.
• Di Nunno, Giulia (2022). Horizon risk and fully-dynamic risk measures.
• Di Nunno, Giulia (2022). Optimal control of Volterra type equations: from finite to infinite dimensions and return.
• Di Nunno, Giulia (2022). Fully-dynamic risk measures: time-consistency, horizon risk, and relations with BSDEs and BSVIEs.
• Di Nunno, Giulia (2022). Stochastic games for Volterra time-changed Lévy dynamics.
• Di Nunno, Giulia (2022). Sandwiched SDEs with unbounded drift driven by Hölder noises.
• Ortiz-Latorre, Salvador (2022). High order discretizations to the nonlinear filtering problem.
• Ortiz-Latorre, Salvador (2022). Machine learning applied to the stochastic filtering problem .
• Grochowicz, Aleksander; van Greevenbroek, Koen; Benth, Fred Espen & Zeyringer, Marianne (2022). Intersecting near-optimal spaces for robust energy systems.
• Zeyringer, Marianne; Benth, Fred Espen; Roithner, Maximilian; Grochowicz, Aleksander & Sirotko-Sibirskaya, Natalia (2022). Climate-resilient net-zero energy system design.
• van Greevenbroek, Koen & Grochowicz, Aleksander (2022). Effect of different weather years on policymakers’ decision space.
• Grochowicz, Aleksander (2022). Intersecting near-optimal spaces for more resilience against weather variability.
• Petersson, Andreas Erik (2022). SPDE bridges with observation noise and their spatial approximation.
• Petersson, Andreas Erik (2022). Interpolation of noise in finite element approximation of stochastic PDEs.
• Petersson, Andreas Erik (2022). Numerical approximation of the heat modulated infinite dimensional Heston model.
• Petersson, Andreas Erik (2022). Numerical approximation of the heat modulated infinite dimensional Heston model.
• Petersson, Andreas Erik (2022). ​Interpolation of noise in finite element approximation of stochastic PDEs.
• Petersson, Andreas Erik (2022). Interpolation of noise in the finite element approximation of the HEIDIH model.
• Dordevic, Jasmina (2022). "On reflected backward stochastic differential equations driven by time-changed Lévy noise”.
• Dordevic, Jasmina (2022). “Time-changed Lévy process and application of stopping problems to RBSDEs“.
• Dordevic, Jasmina (2022). “Interference of time-change Lévy noises on characterisation of reflected backward stochastic differential equations“.
• Dordevic, Jasmina (2022). “Reflected Backward Stochastic Differential Equations with Time-change Lévy noises.”.
• Dordevic, Jasmina (2022). “Modelling of epidemics with time-changed Lévy process”.
• Dordevic, Jasmina (2022). “Backward stochastic differential equations”.
• Savku, Emel (2022). An Application of Nonzero-Sum Stochastic Differential Games in Finance.
• Benth, Fred Espen (2022). Pricing options on flow forwards by neural networks in Hilbert space.
• Savku, Emel (2022). An Application of Markov Regime-Switching Models: Bancassurance.
• Savku, Emel (2022). A Constrained Nonzero-Sum Game Application: Bancassurance.
• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2022). Stochastic Modeling of Stratospheric Temperature. Show summary

  This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

• Savku, Emel (2022). An Application of Stochastic Differential Games with Lagrange Multipliers: Bancassurance.
• Savku, Emel (2022). A Constrained Nonzero-Sum Stochastic Differential Game Application.
• Savku, Emel (2022). An Application of Stochastic Differential Games with Lagrange Multipliers:Bancassurance.
• Savku, Emel (2022). A constrained stochastic differential game application: Bancassurance.
• Harang, Fabian Andsem (2022). Pathwise regularization by noise for SDEs and SPDEs with multiplicative noise.
• Benth, Fred Espen (2022). Modellering av risiko i energisystemer.
• Yurchenko-Tytarenko, Anton (2021). Standard and fractional ROU processes as the limits of square roots of CIR processes.
• Di Nunno, Giulia (2021). Maximum principles for stochastic time-changed Volterra games.
• Di Nunno, Giulia (2021). Sensitivity analysis in the infinite dimensional Heston model.
• Di Nunno, Giulia (2021). Infinite dimensional Heston model and sensitivity analysis.
• Di Nunno, Giulia (2021). Rough volatility: SDE with unbounded drift driven by Hölder continuous noise.
• Di Nunno, Giulia (2021). Sensitivity analysis in the infinite dimensional Heston model.
• Di Nunno, Giulia (2021). Optimal portfolios in markets with memory.
• Petersson, Andreas Erik (2021). Approximation of SPDE covariance operators by finite elements: A semigroup approach.
• Petersson, Andreas Erik (2021). SPDE bridges with observation noise and their spatial approximation.
• Dordevic, Jasmina (2021). “Backward stochastic differential equations with interaction”.
• Dordevic, Jasmina (2021). “Stochastic analysis of spread & preventions in case of SARS-CoV-2 virus”.
• Dordevic, Jasmina (2021). “Clark representation for random measures”.
• Nunno, Giulia Di (2021). On time changed Lévy noises in modelling, dynamics and control.
• Lindstrøm, Tom Louis (2021). Matematikk og virkelighet: Om å beregne det som ikke kan måles.
• Lindstrøm, Tom Louis (2021). Programmering i matematikkfaget.
• Lindstrøm, Tom Louis (2021). Utforsking i matematikk: Trampoline eller hengemyr?
• Lindstrøm, Tom Louis (2021). Implementation of Computational Thinking at the University of Oslo.
• Harang, Fabian Andsem (2021). Pathwise regularization by noise for SDEs and SPDEs with multiplicative noise.
• Harang, Fabian Andsem (2021). Introduction to Rough Paths Theory.
• Harang, Fabian Andsem (2021). Log-modulated fractional Brownian motion and super rough volatility. .
• Benth, Fred Espen & Zeyringer, Marianne (2021). Uncertain Energy Systems.
• Benth, Fred Espen (2021). Pathwise Gaussian Volterra processes in Hilbert space.
• Benth, Fred Espen & Zeyringer, Marianne (2021). Uncertain energy systems.
• Benth, Fred Espen & Zeyringer, Marianne (2021). Er de rekordhøye strømprisene verdt det? Forskning.no. ISSN 1891-635X.
• Midtfjord, Alise Danielle (2021). A Machine Learning Approach to Assess Runway Conditions Using Weather Data.
• Midtfjord, Alise Danielle (2021). A Machine Learning Approach to Safer Airplane Landings.
• Midtfjord, Alise Danielle (2021). A decision support system for safer airplane landings: predicting runway conditions using XGBoost and explainable AI.
• Savku, Emel (2021). An Application of Stochastic Maximum Principle with Regimes and Memory.
• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2021). Stochastic modelling of stratospheric temperature.
• Nunno, Giulia Di (2021). Maximum principles for stochastic time-changed Volterra games.
• Nunno, Giulia Di (2021). Sensitivity analysis in the infinite dimensional Heston model.
• Nunno, Giulia Di; Benth, Fred Espen & Simonsen, Iben Cathrine (2021). Infinite dimensional Heston model and sensitivity analysis.
• Nunno, Giulia Di & Yurchenko-Tytarenko, Anton (2021). Rough volatility: SDE with unbounded drift driven by Hölder continuous noise.
• Nunno, Giulia Di (2021). Sensitivity analysis in the infinite dimensional Heston model.
• Nunno, Giulia Di (2021). Optimal portfolios in markets with memory.
• Benth, Fred Espen (2021). Hedging volumetric risk in renewable energy markets.
• Benth, Fred Espen & Schrader, Simon Elias (2021). Send krafta til Tyskland. Klassekampen. ISSN 0805-3839.
• Dordevic, Jasmina (2021). "Clark representation for random measures".
• Giordano, Michele & Yurchenko-Tytarenko, Anton (2021). Optimal control in linear stochastic advertising models with memory.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Stochastic volatility modelling via sandwiched processes with Volterra noise.
• Dordevic, Jasmina (2021). Effect of Additive Perturbations on the Solution of Reflected Backward Stochastic Differential Equations. In Carpentieri, Bruno (Eds.), Recent Developments in the Solution of Nonlinear Differential Equations. IntechOpen. ISSN 978-1-83968-657-3. doi: %20http:/dx.doi.org/10.5772/intechopen.95872. Show summary

  This chapter has as a topic large class of general, nonlinear reflected backward stochastic differential equations with a lower barrier, whose generator, final condition as well as barrier process arbitrarily depend on a small parameter. The solutions of these equations which are obtained by additive perturbations, named the perturbed equations, are compared in the L p -sense, p ∈ ] 1 , 2 [ , with the solutions of the appropriate equations of the equal type, independent of a small parameter and named the unperturbed equations. Conditions under which the solution of the unperturbed equation is L p -stable are given. It is shown that for an arbitrary a > 0 there exists t a ≤ T , such that the L p -difference between the solutions of both the perturbed and unperturbed equations is less than a for every t ∈ t a T .

• Savku, Emel (2021). Stochastic Optimal Control Techniques for a Regime-Switching Model with Applications in Finance.
• Petersson, Andreas Erik (2021). Approximation of SPDE covariance operators by finite elements: A semigroup approach.
• Dahl, Kristina Rognlien & Eyolfsson, Heidar (2021). Self-exciting jump processes as deterioration models.
• Savku, Emel (2021). A Nonzero-sum Game Formulation for a Markov Regime-Switching Portfolio Strategy.
• Savku, Emel (2021). Stochastic Maximum Principle with Regimes and Memory.
• Savku, Emel (2021). Stochastic Differential Games via Dynamic Programming Principle with Regimes.
• Eggen, Mari Dahl (2021). Time Series and CNNs - Three articles on the topic.
• Midtfjord, Alise Danielle (2021). The Fundamentals of AI. Show summary

  What's Artificial Intelligence (AI)? What's the difference between AI and machine learning (ML), as they're sometimes used interchangeably? What's the current state of AI? What is AI capable of these days and what not? What are the societal impact and implications of AI? These are questions we will discuss in the upcoming event co-organized by Pint of Science Norway (http://pintofscience.no/) and Oslo AI (http://oslo.city.ai/). We've gathered a panel of experts coming from academia and industry. They will demystify AI for you and answers all your questions.

• Savku, Emel (2021). Portfolio Strategies via Stochastic Differential Games with Regimes.
• Savku, Emel (2021). Stochastic Differential Games within the framework of Regime-Switches.
• Benth, Fred Espen (2021). Pathwise Gaussian Volterra processes in Hilbert space.
• Di Nunno, Giulia (2020). Infinite dimensional Heston model: pricing and sensitivity analysis .
• Di Nunno, Giulia (2020). Stochastic control for Volterra equations driven by time-changed noises .
• Di Nunno, Giulia (2020). Stochastic control for Volterra equations driven by time-changed noises .
• Di Nunno, Giulia (2020). Stochastic control for Volterra equations driven by time-changed noises.
• Midtfjord, Alise Danielle (2020). Development of a data-driven warning system for runway conditions.
• Midtfjord, Alise Danielle (2020). Estimating Runway Friction Using Flight Data.
• Nunno, Giulia Di (2020). Infiite dimensional Heston model: pricing and sensitivity analysis.
• Nunno, Giulia Di (2020). Stochastic control for Volterra equations driven by time-changed noises .
• Nunno, Giulia Di (2020). Stochastic control for Volterra equations driven by time-changed noises.
• Nunno, Giulia Di (2020). Stochastic control for Volterra equations driven by time-changed noises.
• Dordevic, Jasmina (2020). "Perturbation effects on Backward Doubly Stochastic Differential Equations & their applications".
• Dordevic, Jasmina (2020). "A stochastic epidemical model for the spread of HIV virus".
• Dordevic, Jasmina (2020). "Perturbation problems of BSDEs their application".
• Dordevic, Jasmina (2020). "Connection of BSDEs with SPDEs, Feymann Kac formula".
• Giordano, Michele & Nunno, Giulia Di (2020). Lifting of Volterra processes: optimal control and HJB equations.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2020). Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
• Petersson, Andreas Erik (2020). Approximating the covariance operator of the solution to the stochastic wave equation .
• Petersson, Andreas Erik (2020). Approximating the covariance operator of the solution to the stochastic wave equation.
• Petersson, Andreas Erik (2020). Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs.
• Ortiz-Latorre, Salvador & Crisan, Dan (2020). High order discretizations to the nonlinear filtering problem.
• Harang, Fabian Andsem (2020). Infinitely regularizing paths, and regularization by noise.
• Amine, Oussama; Mansouri, Abdol-Reza & Proske, Frank Norbert (2020). Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths.
• Lindstrøm, Tom Louis (2020). Digital undervisning i matematikk: Erfaringer fra Universitetet i Oslo.
• Lindstrøm, Tom Louis (2020). Fagfornyelsen og svaktpresterende elever.
• Lindstrøm, Tom Louis (2020). Matematikk som inspirerer.
• Lindstrøm, Tom Louis (2020). Hva gjør en anvendt matematiker?
• Lindstrøm, Tom Louis (2020). Lineæralgebraens ikke-lineære historie.
• Eggen, Mari Dahl (2020). The ETAS model.
• Eggen, Mari Dahl (2020). Stratospheric Temperature Modelling.
• Eggen, Mari Dahl (2020). Earthquake and Stratospheric Dynamics Modelling.
• Eggen, Mari Dahl (2020). The LIBOR Forward Rate in a HJM-Lévy Framework.
• Eggen, Mari Dahl (2020). The LIBOR Forward Rate in a HJM-Lévy Framework.
• Dahl, Kristina Rognlien & Huseby, Arne (2020). Environmental contours and optimal design.
• Dahl, Kristina Rognlien (2020). The SCROLLER project and a subproject: Optimal design.
• Midtfjord, Alise Danielle (2020). Estimating Runway Friction Using Flight Data. Show summary

  During the winter season, contamination of runway surfaces with snow, ice, or slush causes potential economic and safety threats for the aviation industry. The presence of these materials reduces the available tire-pavement friction needed for retardation and directional control. Therefore, pilots operating on contaminated runways need accurate and timely information on the actual runway surface conditions. Avinor, the company that operates most civil airports in Norway, have developed an integrated runway information system, called IRIS, currently used on 16 Norwegian airports. The system uses a scenario approach to identify slippery conditions. In order to validate the scenario model, it is necessary to estimate runway friction. The present paper outlines how this can be done using flight data from the Quick Access Recorder (QAR) of Boeing 737-600/700/800 NG airplanes. Data such as longitudinal acceleration, airspeed, ground speed, flap settings, engine speed, brake pressures are sampled at least each second during landings. The paper discusses some of the challenges with this. In particular, issues related to calibration of data are considered, and two different regression methods are compared.

• Di Nunno, Giulia; Arici, Francesca & Cherubini, Anna Maria (2020). Going beyond the boundaries: An interview with Giulia Di Nunno. [Internet]. European Women in Mathematics.
• Di Nunno, Giulia & Isaksen, Karoline Kvellestad (2020). Alumni Spotlight: Giulia Di Nunno. [Internet]. Newsletter CAS Oslo.
• Di Nunno, Giulia (2020). Work in Research in Norway and Scandinavia.
• Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations. Show summary

  Based on a joint work with Giulia Di Nunno

• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Hölder noises.
• Schroers, Dennis (2020). Copulas and Sklar’s Theorem in Infinite Dimensions. Show summary

  Copulas describe statistical dependence between the components of multivariate random variables in full generality by virtue of Sklar’s theorem. Although they are used and defined for certain infinite dimensional objects (e.g. Gaussian processes in [WG10], Markov processes in [DNO92], [Ibr09] and [L10], or copulas in Hilbert spaces in [HR17]) there is no prevalent notion of a copula as an infinite dimensional law that unifies these concepts. To this end we define copulas as probability measures on product spaces RI for some index set I and formulate Sklar’s theorem in this general setting. An important application is the task of modeling the inherent dependence of random variables in function spaces. In Banach spaces (or more general topological vector spaces) already the notion of marginals becomes ambiguous: Take the example of the space C[0,1]. it is possible to emded this space into the product space R[0,1] of real functions on [0,1] via (1) f ↦ ( f (x))x∈[0,1] At the same time, the existence of a Schauder basis in this space makes it possible to embded it into the space RN of real sequences via
 (2) f ↦ (en( f ))n∈N for the coefficient functionals (en)n∈N of the Schauder basis. Both embeddings lead to reason- able notions of marginals of a measure μ on C[0,1], either as the laws (μ(δ−1⋅) for the −1 x x∈[0,1] evaluation functionals δxh = h(x), as well as (μ(en ⋅)n∈N. For this reason, copula on function spaces have to be considered for each of such a proper dual subset separately, depending on the respective modeling task. In finite dimensions the second part of Sklar’s Theorem enables us to construct probability measures by merging arbitrary marginals and dependence structures (in form of copulas). This simple construction cannot be transferred into the infinite dimensional setting of function spaces without any problems: Taking a set of marginals (μ(δ−1⋅) in terms of the function x x∈[0,1] embedding (1) on C[0,1], and a set of absolutely continuous marginal distributions (Ft)t∈[0,1], we need these marginals to be continuous in distribution, that is t ↦ Ft(x) has to be continuous for each x ∈ R. This is clearly not the case for every choice of marginals and the constructed measure would rather be a cylindrical premeasure on C[0,1]. We will therefore provide criteria to decide if the construction induced by the second part of Sklar’s theorem yields certain properties like the regularity of paths and culminates in a real probability law in a function space. In addition, following [CARTD93] and [AJ14], we link our concept of copulas to Wasserstein distances. Namely, underlying copulas of probability laws in lp -sequence spaces with finite pth moment effectively solve a marginal-restricted optimisation problems in the pth Wasserstein space.

• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Holder noises.
• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Hölder noises. Show summary

  We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above some continuous function or has continuous upper and lower bounds. Under some additional assumptions on the noise, we prove that the solution has moments of all orders. Additionally, numeric schemes for the solution are considered. As illustrations of our approach, generalised CIR and CEV processes will be discussed. This talk is based on joint work with Giulia Di Nunno and Yuliya Mishura.

• Schroers, Dennis (2020). Copulas and Sklar's Theorem in Infinite Dimensions. Show summary

  Copulas describe statistical dependence between the components of multivariate random variables in full generality by virtue of Sklar’s theorem. Although they are used and defined for certain infinite dimensional objects (e.g. Gaussian processes, Markov processes or infinite dimensional Archimedean copulas) there is no prevalent notion of a copula as an infinite dimensional law that unifies these concepts. To this end we define copulas as probability measures on product spaces and prove Sklar’s theorem in this general setting. Afterwards we use this result on Banach spaces to construct cylindrical probability measures with predefined marginals and underlying copula. This induces the functional analytic problem of finding criteria in which cases the obtained cylindrical law induces a real probability measure, which is in general difficult to decide. We solve this problem in the p-Wasserstein space on the space of p-summable sequences (including separable Hilbert spaces) and show that copulas effectively solve a restricted optimal coupling problem.

• Schroers, Dennis (2020). Sklar's Theorem in Infinite Dimensions.
• Yurchenko-Tytarenko, Anton (2020). SDEs with unbounded drift driven by Holder noises. Show summary

  In this research, we consider a stochastic differential equation with drift having singularity in zero and an additive noise being a fractional Brownian motion with an arbitrary Hurst parameter. Under some assumptions, existence, uniqueness and positivity of the solution are proved, finiteness of the moments of all orders (including the negative ones) is obtained. As examples, we provide fractional generalisations of the CIR and CEV processes and, using the finiteness of their negative moments, prove convergence of the corresponding backward Euler-type schemes. Separately, we discuss possible extensions of the obtained results including replacing the fractional Brownian motion with general Holder-continuous Volterra process.

• Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations. Show summary

  We want to maximize a performance functional, with dynamics of the underlying forward process of Volterra type. Due to this assumption, the system is not Markovian, and one cannot apply directly the dynamic programming principle (DPP). In order to recover the DPP, we introduce a lift that allows us to get some Markov properties by rewriting the forward process' dynamics in a Banach space setting. Once we reformulated the problem in the new setting, we deduce a DPP for the lifted problem and obtain the corresponding infinite dimensional HJB equations. We go back to the initial real valued problem and characterize the optimal control of the original problem in terms of the solution of the lifted one. Examples and applications will be presented. Joint work with Giulia di Nunno

• Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations. Show summary

  Based on a joint work with Giulia di Nunno

• Harang, Fabian Andsem (2020). C^\infty regularization of ODEs perturbed by noise.
• Giordano, Michele (2020). Maximum Principles for Stochastic Time Changed Volterra Games. Show summary

  We establish a framework for the study of forward-backward stochastic Volterra integral games (FBSVIG) driven by time-changed Lévy noises. We use a maximum principle approach in order to find the Nash equilibriums of a two player game based on a forward equation and a backward equation for each player. Since we work with time change, we deal with two information flows and we consider one filtration to have partial information respect to the other. Examples will be provided. Joint work with Giulia di Nunno Based on a joint work with Giulia di Nunno

• Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations. Show summary

  Based on a joint work with Giulia Di Nunno

• Dahl, Kristina Rognlien (2020). The SCROLLER project A Stochastic ContROL approach to machine Learning with applications to Environmental Risk models.
• Dahl, Kristina Rognlien (2020). FBSDE games with delay & noisy memory.
• Harang, Fabian Andsem (2020). Volterra Equations driven by Rough Noise.
• Harang, Fabian Andsem (2020). Volterra Equations Driven by Rough Signals.
• Harang, Fabian Andsem (2020). Infinitely regularising paths and regularisation by noise.
• Midtfjord, Alise Danielle (2020). Explainable Artificial Intelligence (XAI). Show summary

  As the use of “black box” algorithms such as deep learning increases rapidly, several challenges related to ethics and law arise. Explainable Artificial Intelligence (XAI) addresses these issues by creating understandable explanations of how and why AI systems arrive at their decisions, and we will try out some of these methods during this workshop.

• Midtfjord, Alise Danielle (2020). Explainable Artificial Intelligence: How to make AI responsible. Show summary

  As the use of “black box” algorithms such as deep learning increases rapidly, several challenges related to ethics and law arise. These systems are not capable of explaining their decisions and actions to human users, making it difficult to make sure they follow the laws are morals of our society. Explainable Artificial Intelligence (XAI) addresses these issues by creating understandable explanations of how and why AI systems arrive at their decisions. In this presentation you will learn about some of the moral challenges rising with the use of artificial intelligence, what explainable artificial intelligence is and how it can address a lot of these challenges and contribute to creating trustworthy and responsible AI.

• Ortiz-Latorre, Salvador & Lagunas, Marc (2019). A Hull-White Formula for a Fractional Volatility Lévy Model.
• Proske, Frank Norbert (2019). Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial nise.
• Di Nunno, Giulia (2019). Excursus on time change in stochastic analysis and control.
• Huseby, Arne; Vanem, Erik & Barbosa, Maria Hjelset (2019). Evaluating probabilistic properties of environmental contours for mixtures of distributions. Show summary

  Environmental contours are widely used as a basis for e.g., ship design, especially in early design phases. The traditional approach to such contours is based on the well-known Rosenblatt transformation. In the present paper we present a numerical method making it possible to apply the inverse Rosenblatt transformation to mixtures of distributions. Due to the effects of this transformation the probabilistic properties of the resulting environmental contour can be distorted. Based on a precise definition of the concept of exceedance probability, valid for all types of environmental contours, we show how to evaluate a given contour and adjust it so that it gets the desired properties. The methods are illustrated by a numerical example.

• Huseby, Arne (2019). When does a convex environmental contour exist? Show summary

  Environmental contours are widely used as a basis for e.g., ship design, especially in early design phases. The traditional approach to such contours is based on the well-known Rosenblatt transformation. Unfortunately, due to the non-linearity of this transformation, the resulting contour may not have the desired probabilistic interpretation. Recent methods for constructing such contours include Monte Carlo which in principle produce convex contours with a constant exceedence probability in all tail directions. Due to numerical instabilities, however, such contours typically contain small irregularities or loops. The presence of such loops is closely related to the mathematical conditions for the existence of a convex contour. In this presentation we present a precise mathematical existence condition as well as a smoothing method which can be used to eliminate possible loops.

• Huseby, Arne; Kalinowska, Martyna & Abrahamsen, Tobias (2019). Multistate systems and importance measures. Show summary

  Within the field of reliability multistate systems represent a natural extension of the classical binary approach. Various classes of multistate systems have been studied extensively with emphasis on extending the properties of binary systems. In this brief note we instead extend the theory by focussing on the physical properties of such systems. We argue that this approach will make it easier to adopt the methodology as the analyst do not need to encode various physical quantities using an abstract integer scale. Within this framework we introduce and compare two measures of importance defined for repairable multistate systems. Both measures can be viewed as direct generalisations of the classical Birnbaum measure.

• Benth, Fred Espen (2019). Stochastic volatility in energy and commodity markets.
• Vanem, Erik & Huseby, Arne (2019). Environmental contours for safe design of ships and other marine structures.
• Di Nunno, Giulia (2019). ICIAM 2019 Su Buchin - Prize Prof. Giulia di Nunno. [TV]. WebsEdgeEducation.
• Di Nunno, Giulia & Salomon, Mónica G. (2019). Hay matemáticos de primer nivel trabajando a destajo en África. [Newspaper]. El Pais.
• Di Nunno, Giulia & Natalini, Roberto (2019). Interview by Roberto Natalini with Giulia Di Nunno, 2019 Su Buchin Prize Winner. [Internet]. DIANOIA.
• Di Nunno, Giulia (2019). Mathematics, Society, Economy and Development.
• Di Nunno, Giulia (2019). Optimal strategies in a market with memory. Show summary

  We consider a market model driven by Volterra type dynamics driven by a time-changed Levy noise. These dynamics allow both for memory features and clustering effects in the trading times. In this framework, we study an optimal portfolio problem, which is then tackled via maximum principle. To produce such results we use different kind of information flows that take care of the time-change in adequate way and we rely on the non-anticipating stochastic derivative for random fields. Moreover, we study the solutions of Volterra type SDEs and Volterra type BSDEs driven by time-changed Levy noises. Talk based on joint work with Michele Giordano, UiO.

• Di Nunno, Giulia (2019). Time-change in modelling, stochastic calculus and control. Show summary

  Time change is a powerful technique for generating noises and providing flexible models. Its main idea stands in the representation of complicated stochastic structures by some known processes and a randomly perturbed time line. We shall provide an excursus through related stochastic calculus, chaos structure and information, integral representations and stochastic differentiation. These will then be applied to backward stochastic differential equations and optimal control problems. Motivation of our work is taken from stochastic finance.

• Di Nunno, Giulia (2019). Martingale random fields in time change models, the role of information in optimal portfolio problems.
• Ortiz-Latorre, Salvador & Crisan, Dan (2019). High order discretizations to the nonlinear filtering problem.
• Lagunas Merino, Marc; Harang, Fabian Andsem & Ortiz-Latorre, Salvador (2019). Self-Exciting Multifractional Processes (SEM) Processes. Show summary

  Abstract. We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this through a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as give bounds on the p-order moments, for all p>=1. We show convergence of an Euler-Maruyama scheme for the process, and also give the rate of convergence, which is depending on the self-exciting dynamics of the process. Moreover, we discuss different applications of this process, and give examples of different functions to model self-exciting behavior.

• Giordano, Michele (2019). A Maximum principle for Volterra Time Changed Processes. Show summary

  We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by time-changed Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$-predictable case we can find a solution by projecting the results obtained for the $G$-predictable case onto the $F$-predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the non-anticipating derivative introduced and for martingale random fields as integrators. The use of the non-anticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

• Giordano, Michele (2019). A Maximum principle for Volterra Time Changed Processes. Show summary

  We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by time-changed Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$-predictable case we can find a solution by projecting the results obtained for the $G$-predictable case onto the $F$-predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the non-anticipating derivative introduced and for martingale random fields as integrators. The use of the non-anticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

• Giordano, Michele (2019). A Maximum principle for Volterra time changed processes. Show summary

  We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by time-changed Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$-predictable case we can find a solution by projecting the results obtained for the $G$-predictable case onto the $F$-predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the non-anticipating derivative introduced and for martingale random fields as integrators. The use of the non-anticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

• Giordano, Michele (2019). A Maximum Principle for Volterra Time Changed Processes. Show summary

  We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by time-changed Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$-predictable case we can find a solution by projecting the results obtained for the $G$-predictable case onto the $F$-predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the non-anticipating derivative introduced and for martingale random fields as integrators. The use of the non-anticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

• Giordano, Michele (2019). A Maximum Principle for Volterra Time Changed Processes . Show summary

  We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by time-changed Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$-predictable case we can find a solution by projecting the results obtained for the $G$-predictable case onto the $F$-predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the non-anticipating derivative introduced and for martingale random fields as integrators. The use of the non-anticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

• Harang, Fabian Andsem (2019). Volterra equations driven by rough signals (2).
• Harang, Fabian Andsem (2019). Volterra equations driven by rough signals.
• Harang, Fabian Andsem (2019). A multi parameter sewing lemma, and applications.
• Harang, Fabian Andsem (2019). A Multiparameter Sewing Lemma with applications.
• Benth, Fred Espen (2019). Stochastic volatility in commodity markets.
• Benth, Fred Espen (2019). Stochastic volatility in energy markets.
• Lindstrøm, Tom Louis (2019). Ultrafilter convergence of stochastic processes.
• Dahl, Kristina Rognlien (2019). Robotene kommer! Kunstig intelligens. Maskinlæring. Big data.
• Dahl, Kristina Rognlien (2019). Math vs The World: Mathematical models. Big data. Reality.
• Dahl, Kristina Rognlien (2019). Mattementormotivasjon.
• Dahl, Kristina Rognlien (2019). Å studere matematikk ved UiO.
• Ortiz-Latorre, Salvador & Crisan, Dan (2018). High order discretizations to the nonlinear filtering problem.
• Huseby, Arne & Rabbe, Marit (2018). Optimal warning scenarios for slippery runways. Show summary

  Slippery runways represent a significant risk to aircrafts especially during the winter season. In order to apply the appropriate braking action, the pilots need reliable information about the runway conditions. Unfortunately the accuracy of runway reports can sometimes be unsatisfactory. In order to obtain more precise and up-to-date information about the current conditions, a warning system based on various types of weather data was suggested by Huseby & Rabbe (2012). See also Huseby & Rabbe (2008) and Huseby et al. (2010). The system is based on a set of scenarios known to cause slippery conditions. By monitoring meteorological parameters like air and ground temperature, humidity, visibility and precipitation, and comparing these to the given scenarios, the system can issue warnings to the ground personnel. This system is currently being used on 16 Norwegian airports. In the present paper this warning system is reviewed. Ideally, the warning system should issue warnings whenever the estimated runway conditions are medium or worse. At the same time the system should not issue warnings when the runway conditions are good. Thus, there are two types of errors we need to take into consideration. Type 1 errors occur when the system does not issue a warning even though the conditions are medium or worse, while type 2 errors occur if a warning is issued when the conditions are good. When designing the system, we need to find the optimal balance between these types of errors taking into account that a type 1 error to a certain degree is considered to be worse than a type 2 error. The paper describes how the system can be optimized using a combination of weather and flight data

• Di Nunno, Giulia (2018). On fully-dynamic risk-indifference pricing: time-consistency and other properties. Show summary

  Risk-indifference pricing is proposed as an alternative to utility indifference pricing, where a risk measure is used instead of a utility based preference. In this, we propose to include the possibility to change the attitude to risk evaluation as time progresses. This is particularly reasonable for long term investments and strategies. Then we introduce a fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. The risk-indifference pricing system is studied from the point of view of its properties as a convex price system. We tackle questions of time-consistency in the risk evaluation and the corresponding prices. This analysis provides a new insight also to time-consistency for ordinary dynamic risk-measures. Our techniques and results are set in the representation and extension theorems for convex operators. We shall argue and finally provide a setting in which fully-dynamic risk-indifference pricing is a well set convex price system. The presentation is based on joint works with Jocelyne Bion-Nadal.

• Di Nunno, Giulia (2018). Levy driven Volterra processes: approximation and integration. Show summary

  Volterra type processes appear in several applications ranging from turbulence, to energy finance, and biological modelling. In general, these processes are not semimartingales and a theory of stochastic integration with respect to such processes is in fact not standard. In this presentation, we consider L\’evy driven Volterra processes and we discuss some recent approaches based on fractional calculus. We study both semimartingale approximations to the Volterra process and approximation to the integral. As illustration, we detail the study of the so-called Gamma-Volterra processes, which is particularly popular in modelling. This is based on joint works with Andrea Fiacco, Erik Karlsen, Yuliya Mishura, Kostia Ralchenko

• Di Nunno, Giulia (2018). On the integration with respect to Volterra type processes. Show summary

  Volterra processes appear in several applications ranging from turbulence, to energy finance, and biological modelling. Volterra processes are in general non-semimartingales and a theory of integration with respect to such processes is in fact not standard. We consider L\’evy driven Volterra processes and we discuss some some recent approaches and results within the framework of Malliavin calculus and fractional calculus. As illustration we consider specifically the so-called Gamma-Volterra processes, which is particularly popular in modelling. This is based on joint works with Andrea Fiacco, Erik Karlsen, Yuliya Mishura, Kostia Ralchenko, Josep Vives

• Di Nunno, Giulia (2018). Stochastic calculus and control for systems driven by time-changed Levy noises.
• Di Nunno, Giulia (2018). Kyle-Backs equilibrium model with a random time of information release. Show summary

  We consider the continuous-time version of Kyle-Back’s model, originally from 1985 and 1992. In Back’s model there is asymmetric information in the market in the sense that there is an insider having information on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. The market makers give prices via a pricing rule, that depends on the total demand and a certain price pressure. In this work we consider both the case of deterministic and stochastic price pressure. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. The presentation is based on joint works with: José Manuel Corcuera (U. Barcelona) and José Fajardo (Brazilian School of Public and Business Administration).

• Di Nunno, Giulia (2018). Integration with respect to Levy driven Volterra processes. Show summary

  Volterra processes appear in several applications ranging from turbulence to energy finance and biological modelling. Volterra processes are in general non-semimartingales and a theory of integration with respect to such processes is in fact not standard. We present some recent results within the framework of fractional calculus and Malliavin Calculus. As illustration we consider specifically the so-called Gamma-Volterra processes. The presentation is based on joint works with: Andrea Fiacco, Erik H. Karlsen and Josep Vives.

• Di Nunno, Giulia (2018). Malliavin Calculus and Applications to Finance.
• Di Nunno, Giulia (2018). A continuous auction model with insiders and random time of information release. Show summary

  In a unified framework we study equilibrium in the presence of an insider having information on the signal of the firm value, which is naturally connected to the fundamental price of the firm related asset. The fundamental value itself is announced at a future random (stopping) time. We consider two cases. First when the release time of information is known to the insider and then when it is unknown also to her. Allowing for very general dynamics, we study the structure of the insider’s optimal strategies in equilibrium and we discuss market efficiency. In particular, we show that in the case the insider knows the information release time, the market is fully efficient. In the case the insider does not know this random time, we see that there is an equilibrium with no full efficiency, but where the sensitivity of prices is decreasing in time according with the probability that the announcement time is greater than the current time. In other words, the prices become more and more stable as the announcement approaches. This is joint work with Jose Manuel Corcuera, Gergely Farkas, Bernt Øksendal

• Di Nunno, Giulia (2018). On the integration with respect to Volterra processes: fractional calculus and approximation.
• Di Nunno, Giulia (2018). Fully dynamic risk-indifference pricing and no-good-deal bounds. Show summary

  In an incomplete market with no a priori assumption on the underlying price dynamics, we focus on the problem of derivative pricing from the seller's perspective. We consider risk indifference pricing as an alternative to the classical utility indifference, so that the actual evaluations are done via risk measures. In addition we propose a fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic risk measure which extends the one of dynamic risk measure by adding the actual possibility of changing the risk perspectives over time. This entails an analysis on the questions of time-consistency in the risk and then the price evaluations. The framework proposed fits well the study of both short and long term investments. In this framework we study whether the risk indifference criterion actually provides a proper convex price system. We shall see that some conditions have to be fulfilled. Then we consider the relationship of fully dynamic risk-indifference price with no-good-deal bounds. We recall that no-good-deal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fully dynamic risk measure so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. In this way no-good-deal bounds provide a way to select the risk measures to obtain a proper fully-dynamic risk-indifference price system. The presentation is based on various joint works with Jocelyne Bion-Nadal.

• Di Nunno, Giulia (2018). Kyle-Back’s model with a random horizon. Show summary

  The continuous-time version of Kyle (1985)) developed by Back (1992)) is here studied. In Back’s model there is asymmetric information in the market in the sense that there is an insider having infor- mation on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium.

• Dahl, Kristina Rognlien (2018). Buffered environmental contours.
• Benth, Fred Espen (2018). Stochastic volatility modeling in power markets.
• Dahl, Kristina Rognlien (2018). An introduction to binary system analysis.
• Dahl, Kristina Rognlien (2018). My career advice (a.k.a. me giving advice about something I don't know).
• Benth, Fred Espen (2018). Cointegration in continuous time.
• Benth, Fred Espen (2018). Polynomial processes in Banach space.
• Di Nunno, Giulia (2018). Stochastic systems with memory, robustness and sensitivity. Show summary

  Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures. We study the case when the driving noises admit jumps provid- ing results on existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. In the case of Brownian driving noise, we consider evaluations based on these models (e.g. the prices of some financial products) and the risks connected to the choice of these models. In particular we focus on the impact of the initial condition on the evaluations. This problem is known as the analysis of sensitivity to the initial condition and, in the terminology of finance, it is referred to as the Delta. In this work the initial condition is represented by the relevant past history of the stochastic functional differential equation. This naturally leads to the redesign of the definition of Delta. We suggest to define it as a functional directional derivative, this is a natural choice. For this we study a repre- sentation formula which allows for its computation without requiring that the evaluation functional is differentiable. This feature is particularly relevant for applications. Our techniques make use of stochastic calculus via regularisations, Malliavin/Skorohod calculus and functional derivatives. The presentation is based on joint works with: D.R. Banos, F. Cordoni, L. Di Persio, H.H. Haferkorn, F. Proske, E.E. Røse.

• Di Nunno, Giulia (2018). Sandwich extensions of linear and convex operators and their applications. Show summary

  We propose some extension theorems for linear and convex operators from $L_p$ spaces to $L_p$ spaces that preserve both minoring and majoring stochastic bounds. We shall see how these extension theorems are applied within the context of pricing in mathematical finance. We discuss in fact the concept of a pricing system, which is in fact a family of such operators that has to preserve some reasonable conditions, including the time-consistency to guarantee that the fundamental economic criteria of the non-arbitrage principle is maintained. Various properties and form of pricing operators are presented. This talk is based on a series of works with various co-authors: Sergio Albeverio (U. Bonn), Jocelyne Bion-Nadal (CNRS Ecole Polytechnique), Inga B. Eide (now at Finanstilsynet), Yuri Rozanov (CNR Milano).

• Di Nunno, Giulia (2018). Kyle-Backs equilibrium model with a random time of information release. Show summary

  The continuous-time version of Kyle (1985)) developed by Back (1992)) is here studied. In Back’s model there is asymmetric information in the market in the sense that there is an insider having infor- mation on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium. The talk is based on joint works with: Jose Manuel Corcuera, Bernt Øksendal, Gergely Farkas

• Bachouch, Achref (2018). Longstaf-Schwarz algorithm for the valuation of American-Bermuda options.
• Agram, Nacira (2018). Mean-field BSDEs and their applications.
• Agram, Nacira (2018). Mean-field BSDEs and their applications.
• Agram, Nacira (2018). Forward/backward stochastic Volterra integral equations and related topics.
• Agram, Nacira (2018). Forward/backward stochastic Volterra integral equations and related topics.
• Agram, Nacira (2018). Forward/backward stochastic Volterra integral equations and related topics.
• Agram, Nacira (2018). Model uncertainty stochastic mean-field control.
• Grochowicz, Aleksander (2024). Resilience and weather uncertainty in energy system models. Universitetet i Oslo. ISSN 1501-7710. Full text in Research Archive
• Grochowicz, Aleksander; Heineken, Daniel & Wennberg, Sondre (2021). The reliability of wind power in the Longyearbyen area. Universitetssenteret på Svalbard. Full text in Research Archive Show summary

  This report in a white paper format was written as part of the course AGF-353/853 "Sustainable Arctic Energy Exploration and Development" at the University Centre in Svalbard (UNIS). --- Within this decade the current energy system in Longyearbyen has to be revolutionised. Right now, it relies entirely on fossil fuels, but in the future it is envisioned to be a front-runner of renewable systems in the Arctic. Due to the polar night and restricted renewable resources, the reliability of wind power is of crucial importance in this transition. Additionally, the permafrost and remote location demand high robustness and simple maintenance. In this report, we analyse on-shore wind potential in three different locations over the previous decade, including an evaluation of stability and extreme events in Svalbard's harsh climate. To ensure long-term success of this transition, we look at interannual, seasonal, and sub-monthly variations that should be included in suitability assessments. Based on our analysis, disregarding this could lead to installations that can jeopardise the stability of the system. With generated input data that we feed into an energy systems model, we find that if one considers interannual variability and a set of different locations, one can ensure a viable and reliable renewable energy system for Longyearbyen, with on-shore wind as a key component.

• Røe, Per; Goodwin, Håvard; Aker, Eyvind; Kvernelv, Vegard Berg & Zdanowicz, Hanna Marta (2021). HAVANA user manual - Version 8.1. Norsk Regnesentral.
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Klemp, Marianne & Binde, Caroline Ditlev (2019). Sammenligning av medikamenter for behandling av Parkinson pasienter. Norsk Regensentral.
• Midtfjord, Alise Danielle & Futsæther, Cecilia Marie (2018). Prediksjon av behandlingsutfall for hode-og halskreft ved bruk av radiomics av PET/CT-bilder. Norwegian University of Life Sciences, Ås.
• Harang, Fabian Andsem (2018). Stability and Regularization of Stochastic Equations Driven by Fractional and Multifractional Noise. Universitetet i Oslo. ISSN 1501-7710.

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