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Probability and Dynamical Systems Seminar
Irreducible convex paving for martingale transports and beyond
Irreducible convex paving for martingale transports and beyond
Organizers
Speaker
Time
Tuesday, November 11, 2025 3:10 PM - 4:10 PM
Venue
A3-1-101
Abstract
The martingale optimal transport problem stems from mathematical finance, but recently it turned out that it is also related to the second-order Beckmann problem, which concerns, in the two-dimensional case, the optimal design of grillages.
Given two probabilities in convex order, I consider the set of martingale transports between them, i.e., the couplings of the given probabilities that are distributions of one-step martingales. I will show that any martingale coupling between two fixed probability measures in convex order is constrainted by a certain partition of the underlying space into so-called irreducible convex components. Moreover, the mass within these components can be moved freely by some martingale transport.
Given two probabilities in convex order, I consider the set of martingale transports between them, i.e., the couplings of the given probabilities that are distributions of one-step martingales. I will show that any martingale coupling between two fixed probability measures in convex order is constrainted by a certain partition of the underlying space into so-called irreducible convex components. Moreover, the mass within these components can be moved freely by some martingale transport.
Speaker Intro
After graduating from the University of Warsaw, Krzysztof Ciosmak joined the Mathematical Institute of the University of Oxford, where he defended my doctoral thesis on Optimal transport and 1-Lipschitz maps, and subsequently held a postdoctoral position. Before joining BIMSA, he held the Fields-Ontario Postdoctoral Fellowship at the University of Toronto and the Fields Institute.