Robust Pricing And Hedging Based On The Duality Form

We always expose ourselves under the model risk when we consider the option pricing and hedging using Black-Scholes models.People are more and more aware that the importance of model risk to the stability of the financial institute recent years,especially after the credit crisis in 2008.Therefore,we are aiming to construct a robust pricing and hedging framework.This paper described a robust pricing and hedging model under incomplete market conditions related to the transport duality.And we mainly set up the duality between the robust price of European option and its minimal super-hedging cost using the optimal transportation duality and the representation theory of the increasing convex functional:(?)Related theory is also claimed when consider martingale transport problem.In addition,we extend the theory to robust hedging of time-dependent financial instruments,and establish the dual form of transportation optimization problem based on stochastic process.After laying out the theory,we have two examples to explain our theory using trinomial model.