On optimal Skorokhod embedding

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this talk, we consider an extension of the weak formulation of the optimal Skorokhod embedding problem. Using the classical convex duality approach together with the optimal stopping theory, we establish some duality. Moreover, based on the duality, we provide an alternative proof of the monotonicity principle proved by Beiglbock, Cox and Huesmann.