The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker at 10:00: Emanuela Rosazza-Gianin (University Bicocca-Milano)
Title: Fully-dynamic risk measures: horizon risk, time-consistency, and relations with BSDEs and BSVIEs
Abstract: In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully-dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully-dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs such as a converse comparison theorem and the dual representation of the associated risk measures.
Joint work with Giulia Di Nunno.
Speaker at 11:00: Dennis Schroers (University of Bonn)
Title: A feasible central limit theorem for realised covariation of SPDEs in the context of functional data
Abstract: Stochastic PDEs are a powerful tool for modeling various phenomena (e.g. in physics, economics, or meteorology) and form now a well-established field of research. In contrast, research on statistical methods for such systems is rather sparse but currently quite active. The infinite-dimensional nature of stochastic PDE implies nontrivial problems for data analysis and ad-hoc implementations of classical techniques, such as principal component analysis are often inconsistent with the imposed dynamics.
One such instance is the factor analysis of infinite-dimensional term structure models, which can in general be formulated as a simple first-order stochastic PDE (Heath-Jarrow- Morton-Musiela equation). We present a volatility-based nonparametric approach for automatic factor detection that just takes into account mild regularity assumptions (such as no-arbitrage in term structure models) and is much more robust with respect to model misspecifications. This is in contrast to the currently available methods for factor analysis on the term structure and is also new to the statistical literature on stochastic PDE. I present implementable techniques and empirical findings for bond markets that directly rely on asymptotic theory derived in joint work with Fred Espen Benth (University of Oslo) and Almut E.D. Veraart (Imperial College).
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.