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.
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页码：4645 / 4692
页数：48
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