Julio Backhoff, Mathias Beiglböck and Sigrid Källblad Martingale Benamou-Brenier: a probabilistic perspective arxiv e-print 1708.04869 2017 https://arxiv.org/abs/1708.04869
Mathias Beiglböck, Alexander M. G. Cox and Martin Huesmann he geometry of multi-marginal Skorokhod embedding arxiv e-print 1705.09505 2017 https://arxiv.org/abs/1705.09505
Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann, Nicolas Perkowski and David J. Prömel Pathwise super-replication via Vovk's outer measure ArXiv e-prints 2015 http://arxiv.org/abs/1504.03644
2014
Mathias Beiglböck, Alexander M.G. Cox and Martin Huesmann Optimal Transport and Skorokhod Embedding ArXiv eprints 2014 http://arxiv.org/abs/1307.3656
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.