The PhD defence will be in Abels utsikt - Niels Henrik Abels hus. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.
Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence.
Trial lecture
September 24th, time: 9:30 am, room 1259 (Abels utsikt).
Stochastic Optimal Control and BSDEs
Main research findings
This thesis develops new numerical methods for backward stochastic differential equations, a class of stochastic equations widely used in mathematical finance and risk modelling. The main idea is to represent uncertain future quantities through a Wiener chaos expansion, which decomposes a random variable into simpler components.
This approach leads to two new numerical schemes. Unlike many existing methods, they do not require the final payoff or outcome to be a function of a finite-dimensional forward model. The thesis proves convergence of both methods and shows how one of them can be implemented using neural networks.
The same framework is used to construct flexible arbitrage-free financial models. These models can approximate a broad class of price dynamics and can be calibrated efficiently to option-market data.
Finally, the thesis studies backward stochastic Volterra equations, which allow for memory effects. New regularity results are proved and used to establish a convergence rate for a numerical approximation.
Candidate contact information
Adjudication committee
- Professor Cornelis W. Oosterlee, Utrecht University
- Professor Athena Picarelli, University of Verona
- Associate Professor Håkon Andreas Hoel, University of Oslo
Supervisors
- Professor Giulia Di Nunno, University of Oslo
- Associate Professor Salvador Ortiz-Latorre, University of Oslo
Chair of defence
Head of Department Arne Bang Husby
Host of the session
Associate Professor Håkon Andreas Hoel, University of Oslo