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M. Beiglböck:
"Cyclical-monotonicity and its offspring";
Talk: International Conference on Stochastic Analysis and Applications: Stochastic Control, information and applications, Hammamet, Tunisia (invited); 2017-10-24 - 2017-10-27.

A fundamental insight in the theory of mass transport is that a transport plan is optimal if and only if its restriction to any finite subset is cyclically monotone. This allows for a powerful geometric approach to the theory of optimal transport plans. An intuition developed in the martingale optimal transport literature is that a similar monotonicity priniciple holds in a much wider context and has applications to a variety of different topics (Skorokhod
embedding problem, mulit-marginal problems, stochastic portfolio theory, Shiryaev´s problem, causal transference plans, the Schrödinger problem, etc.). In this talk we will provide a brief
overview on this line of research.

http://pinguim.uma.pt/Investigacao/Ccm/icsaa17/program/Programme_Hammamet_2017.pdf