The geometry of multi-marginal Skorokhod embedding

Abstract

The martingale optimal transport problem (MOT) is a variant of the optimal transport problem where the coupling is required to be a martingale between its marginals. In dimension one, this problem is well understood for two marginals corresponding to one- step martingales. Via the Dambis-Dubins-Schwarz Theorem the MOT can be translated into a Skorokhod embedding problem (SEP). It turns out that the recently established transport approach to SEP allows for a systematic treatment of all known solutions to (one-dimensional) MOT. We show that the transport approach to SEP extends to a multi-marginal setup. This allows us to show that all known one-marginal solutions have natural multi-marginal coun- terparts. In particular (among other things), we can systematically construct solutions to genuine multi-marginal martingale optimal transport problems. This is joint work with M.Beiglböck and A.Cox