# Dominykas Norgilas - Supermartingale shadow couplings (cancelled)

Dates: | 7 December 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Dominykas Norgilas (University of Michigan) will speak in the Probability seminar.

A classical result of Strassen asserts that given probability measures $\mu,\nu$ on the real line which are in convex-decreasing order, there exists a supermartingale with these marginals, i.e., a random vector $(S_1,S_2)$ such that $S_1\sim\mu$, $S_2\sim\nu$ and $\mathbb{E}S_1=S_1$. However, it is a non-trivial problem to construct particular (or canonical) supermartingales with prescribed marginals. In this talk we introduce a family of such supermartingales, each of which admits canonical characterization in terms of stochastic dominance. We explicit construct the extreme elements (of this family) that solve the martingale optimal transport problem with supermartingale constraints.