Disputas: Olli Wallin

Prøveforelesning

Bedømmelseskomité

Professor Dr. Ralf Korn, Fachbereich Mathematik, Universität Kaiserlslautern, Tyskland
Lecturer, Dr. Thorsten Rheinlander, Department of Statistics, London School of Economics, UK
Associate Professor, Dr. Giulia Di Nunno, Centre of Mathematics for Applicatons , Universitetet i Oslo

Leder av disputas:  Professor Kristian Ranestad

Veileder:  Fred Espen Benth, Kenneth Hvistendahl

Sammendrag

The research in the theses was done at the Centre for Mathematics and Applications, University of Oslo, and belongs in the fields of financial mathematics and control theory.

The theses develops mathematical theory and computational methods for studying the distribution of uncertain cash flows, and pricing and management of financial derivatives in the stock and energy markets. Especially, the main effort in the theses is made to include models that can capture the abrupt changes in the behavior of these markets that at times takes place.

In the first part, probability distributions of integral functionals that arise in many different fields, including insurance and finance are studied. The study extends previously known identities, and tests the applicability of some numerical methods in cases where no explicit solutions can be found.

The second part contributes to the computation of the sensitivity of option prices to changes in different parameters in a model that captures the random behavior of stock market volatility. More specifically, a numerical simulation method that applies Malliavin Calculus is extended to the case of a Barndorff-Nielsen and Shephard model. Some specific examples are studied to test the effectiveness of the method in this setting.

Many financial derivatives contracts include control features that increase the flexibility in decision making of the holder of the contract. The complexity of such contracts typically makes it difficult to derive the value of a contract in an explicit form. However, one can characterize the value as a solution of an equation, and numerical methods can then be applied for their solution. In the theses, new equations for two specific contract structures traded in the stock and energy markets, respectively, are derived. The mathematical theory built in the thesis validates these equations and further forms the basis for insuring that numerical methods based on the equations converge to the true solution. The methodology built allows one to include the possibility of large, sudden movements of market prices.

Kontaktperson

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