PhD Oral Exam - Alexandre Carbonneau, Mathematics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

This thesis studies the problem of pricing and hedging financial derivatives with reinforcement learning. Throughout all four papers, the underlying global hedging problems are solved using the deep hedging algorithm with the representation of global hedging policies as neural networks. The first paper, Equal Risk Pricing of Derivatives with Deep Hedging, shows how the deep hedging algorithm can be applied to solve the two underlying global hedging problems of the equal risk pricing framework for the valuation of European financial derivatives. The second paper, Deep Hedging of Long-Term Financial Derivatives, studies the problem of global hedging very long-term financial derivatives which are analogous, under some assumptions, to options embedded in guarantees of variable annuities. The third paper, Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments, studies derivative prices generated by the equal risk pricing framework for long-term options when shorter-term options are used as hedging instruments. The fourth paper, Deep equal risk pricing of financial derivatives with non-translation invariant risk measures, investigates the use of non-translation invariant risk measures within the equal risk pricing framework.