CONTINUITY OF THE MARTINGALE OPTIMAL TRANSPORT PROBLEM ON THE REAL LINE

• 成果类型: Article
• 署名作者: Wiesel, Johannes
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1928
• 发表日期: 2023
• 页码: 4645-4692
• 关键词: causal transport

摘要

We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the set of martingale couplings with the same marginals. As a corollary we obtain an independent proof of sufficiency of the monotonicity principle established in Beiglbock and Juillet (Ann. Probab. 44 (2016) 42- 106) for cost functions of polynomial growth.