Tak by Ivan Guo, Professor Monash University Melbourne
Title: Robust pricing-hedging duality for American options
Abstract: The field of robust finance is about studying and mitigating model uncertainty. The robust price of a derivative is the maximal expectation under a collection of risk neutral measures, representing the class of candidate models. The robust hedging of a derivative is to find the minimal initial capital required to simultaneously super-replicate the payoff under all candidate models. When these two values are equal, we achieve the so-called robust pricing-hedging duality.
In this talk, we look at the robust pricing-hedging duality of American options in continuous time. The key idea is to enlarge the underlying probability space to include the family of stopping decisions. Then American options can be viewed as European options in this enlarged space. Duality is proven by using stochastic optimal transport techniques in continuous time and path-dependent settings. Extra care is needed to show that optimising over probabilities in the enlarged space is equivalent to solving optimal control and stopping problems in the original space. Relevant concepts will be introduced, including convex duality, path-dependent PDEs, and randomised stopping times.