Duality for a Martingale Transport Problem with Moment Constraints

Alexander V. Kolesnikov; Aleksandra Novikova; Kirill Sokolov

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arXiv · 2609.03187

Duality for a Martingale Transport Problem with Moment Constraints

Alexander V. Kolesnikov·Aleksandra Novikova·Kirill Sokolov

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Abstract

We consider a weak martingale optimal transport problem related to the martingale analogue of the Benamou--Brenier formula. In contrast to the classical setting, the second marginal is not given, but specified only through a finite number of moment constraints of a particular form. For this problem, we derive a finite-dimensional dual formulation and prove the absence of a duality gap under the specified interiority condition on the constraint vector. In addition, we describe the structure of the optimal martingale coupling and its relation to Bass martingales.

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Alexander V. Kolesnikov, Aleksandra Novikova, Kirill Sokolov. 2026-09-02. Duality for a Martingale Transport Problem with Moment Constraints. https://arxiv.org/abs/2609.03187

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