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Localisation for constrained transports: irreducible convex paving and beyond
- Speaker(s)
- Krzysztof Ciosmak
- Affiliation
- Beijing Institute of Mathematical Sciences and Applications
- Language of the talk
- English
- Date
- Dec. 18, 2025, 12:15 p.m.
- Room
- room 3160
- Title in Polish
- Localisation for constrained transports: irreducible convex paving and beyond
- Seminar
- Seminar of Probability Group
Martingale optimal transport is a tool that allows for a model-free pricing of options. 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 constrained 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.
I will also show that these results generalise to measures in order with respect to a complete lattice cone generated by a linear subspace. This provides an affirmative answer to a generalisation of a conjecture proposed by Obłój and Siorpaes regarding polar sets in the martingale transport setting.
