Localisation for constrained transports: irreducible convex paving and beyond

Prelegent(ci)

Krzysztof Ciosmak

Afiliacja

Beijing Institute of Mathematical Sciences and Applications

Język referatu

angielski

Termin

18 grudnia 2025 12:15

Pokój

p. 3160

Tytuł w języku polskim

Localisation for constrained transports: irreducible convex paving and beyond

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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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.

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