ERC Workshop on Optimal Transportation and Applications

A Canonical Martingale Coupling

speaker: Nicolas Juillet (Université de Strasbourg)

abstract: (Joint work with Mathias Beiglböck) According to Strassen, if two real probability measures $\mu$ and $\nu$ are in the convex order i.e., the integral of any convex function $\varphi$ is greater for $\nu$, then there exists a transport plan $\pi$ of ``martingale'' type: $\mu$-almost surely the conditional measure $\pi<sub>x$</sub> has barycenter $x$. We will see that such a measure can enjoy canonical properties when it is chosen as the minimizer of a ``martingale transport problem''. We give other results related to the classical theory of optimal transport.

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