Optimal transport and Skorokhod embedding

12 May 2014
It is well known that several solutions to the Skorokhod problem optimize certain ``cost''- or ``payoff''-functionals. We use the theory of Monge-Kantorovich transport to study the corresponding optimization problem. We formulate a dual problem and establish duality based on the duality theory of optimal transport. Notably the primal as well as the dual problem have a natural interpretation in terms of model-independent no arbitrage theory. In optimal transport the notion of c-monotonicity is used to characterize the geometry of optimal transport plans. We derive a similar optimality principle that provides a geometric characterization of optimal stopping times. We then use this principle to derive several known solutions to the Skorokhod embedding problem and also new ones. This is joint work with Mathias Beiglböck and Alex Cox.
  • Stochastic Analysis Seminar