PhD Oral Exam - Carlos Octavio Perez Mendoza, Mathematics and Statistics

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 explores the use of deep reinforcement learning (DRL) to enhance dynamic option hedging by incorporating forward-looking market information, mitigating speculation, and optimizing portfolio rebalancing frequency. The first paper, Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information, introduces a DRL-based hedging framework that leverages implied volatility surface data, improving hedging performance over traditional methods. The second paper, Is the Difference between Deep Hedging and Delta Hedging a Statistical Arbitrage?, examines whether deep hedging introduces speculative behavior in incomplete markets, demonstrating that proper risk measure selection prevents unwanted speculation. The third paper, Implied-Volatility-Surface-Informed Deep Hedging with Options, extends deep hedging by integrating implied volatility surface-informed decisions, no-trade regions, and multiple hedging instruments, improving cost efficiency and adaptability. This research contributes by defining frameworks that enhance existing techniques for managing risk in financial markets.