Optimal transport and Skorokhod embedding

Martin Huesmann

(Universität Bonn)

Event: ERC Workshop on Optimal Transportation and Applications

Date: Oct 31, 2014, time: 09:00

Abstract. The Skorokhod embedding problem is to represent a given probability as the distribution
of Brownian motion at a chosen stopping time. Over the last 50 years this has become one
of the important classical problems in probability theory and a number of authors have
constructed solutions with particular optimality properties. These constructions employ
a variety of techniques ranging from excursion theory to potential and PDE theory and
have been used in many different branches of pure and applied probability.
We develop a new approach to Skorokhod embedding based on ideas and concepts from
optimal mass transport. In analogy to the celebrated article of Gangbo and McCann on
the geometry of optimal transport, we establish a geometric characterization of Skorokhod
embeddings with desired optimality properties. This leads to a systematic method to
construct optimal embeddings. It allows us, for the first time, to derive all known optimal
Skorokhod embeddings as special cases of one unified construction and leads to a variety
of new embeddings. While previous constructions typically used particular properties of
Brownian motion, our approach applies to all sufficiently regular Markov processes.
This is joint work with Mathias Beiglbck and Alexander Cox