CONTINUITY OF THE MARTINGALE OPTIMAL TRANSPORT PROBLEM ON THE REAL LINE

被引：1

作者：

Wiesel, Johannes ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 6A期

基金：

欧洲研究理事会;

关键词：

Stability; martingale transport; causal transport; weak adapted topology; robust finance; CAUSAL TRANSPORT;

D O I：

10.1214/22-AAP1928

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：4645 / 4692

页数：48

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