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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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Cite

BibTeXRIS
BibTeX
@misc{kolesnikov2026duality,
  title = {{Duality for a Martingale Transport Problem with Moment Constraints}},
  author = {Alexander V. Kolesnikov and Aleksandra Novikova and Kirill Sokolov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03187},
  eprint = {2609.03187},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03187},
}
RIS
TY  - UNPB
TI  - Duality for a Martingale Transport Problem with Moment Constraints
AU  - Alexander V. Kolesnikov
AU  - Aleksandra Novikova
AU  - Kirill Sokolov
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03187
UR  - https://arxiv.org/abs/2609.03187
AB  - 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.
ER  -