Abstracts

In the framework of robust mathematical finance, Dolinsky and Soner (2013) showed that there is no duality gap between the robust hedging of path-dependent European options and a martingale optimal transport problem, when option prices for one maturity are given. In this work, we present a duality result in the setup of multiple maturities. The proof proceeds through a discretisation of the problem. Key steps are to relate the robust hedging problem to a probabilistic super-hedging problem, and to use classical duality result to connect the probabilistic super-hedging problem to a discretised martingale optimal transport problem.
Furthermore, in discrete time, we extend a duality result proved by Beiglbock, Henry-Labordere and Penkner (2011) to markets with bubbles. In both continuous and discrete time, motivated by Mykland (2005)’s idea of having a prediction set of paths (i.e. super-replication of a contingent claim required only for paths falling in the prediction set), we add a path restriction into the pricing and hedging framework.