Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

Entropic Martingale Optimal Transport with Wasserstein Relaxed Marginal Constraints

  • Haowen Chen
  • Renyuan Xu
  • Xin Zhang
Open at sourcePDFDOICite

Abstract

Martingale optimal transport (MOT) is a fundamental framework in robust finance, yet its stability under marginal perturbation no longer holds in high dimensions d≥ 2. In this paper, we introduce Wasserstein-relaxed entropic martingale optimal transport (WEMOT), which combines Wasserstein relaxation of the second marginal with entropy regularization. This formulation ensures stability under perturbations of the marginals, thereby facilitating numerical implementation. We establish strong duality and dual attainment for WEMOT, which leads to efficient Sinkhorn-type algorithms. We further prove a convergence rate of WEMOT to MOT as regularization parameters vanish, and also the quantitative stability of WEMOT with respect to marginal perturbations.

Related

  1. On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport
    Giorgia Bifronte, Armand Ley, Maxime Sylvestre
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  2. Duality for a Martingale Transport Problem with Moment Constraints
    Alexander V. Kolesnikov, Aleksandra Novikova, Kirill Sokolov
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  3. Martingale central limit theorems in p-Wasserstein distance
    Xiao Fang, Yuta Koike, Zi-Yao Su
    arXivPreprintarXiv licenceFull textProbabilityStatisticsarXiv
  4. Quantitative stability of classical, entropic, and doubly entropic Wasserstein barycenters
    Guillaume Carlier, Julien Guérin, Quentin Mérigot
    HALPreprintCC BY-NC-ND 4.0Full textOptimisation & controlHALarXiv
  5. Gaussian Approximation in Wasserstein-p: Markovian Martingale Differences and Stochastic Approximation
    Yixuan Zhang, Qiaomin Xie
    arXivPreprintCC BY 4.0Full textProbabilityStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{chen2026entropic,
  title = {{Entropic Martingale Optimal Transport with Wasserstein Relaxed Marginal Constraints}},
  author = {Haowen Chen and Renyuan Xu and Xin Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08743},
  eprint = {2611.08743},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08743},
}
RIS
TY  - UNPB
TI  - Entropic Martingale Optimal Transport with Wasserstein Relaxed Marginal Constraints
AU  - Haowen Chen
AU  - Renyuan Xu
AU  - Xin Zhang
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08743
UR  - https://arxiv.org/abs/2611.08743
AB  - Martingale optimal transport (MOT) is a fundamental framework in robust finance, yet its stability under marginal perturbation no longer holds in high dimensions d≥ 2. In this paper, we introduce Wasserstein-relaxed entropic martingale optimal transport (WEMOT), which combines Wasserstein relaxation of the second marginal with entropy regularization. This formulation ensures stability under perturbations of the marginals, thereby facilitating numerical implementation. We establish strong duality and dual attainment for WEMOT, which leads to efficient Sinkhorn-type algorithms. We further prove a convergence rate of WEMOT to MOT as regularization parameters vanish, and also the quantitative stability of WEMOT with respect to marginal perturbations.
ER  -