Continuity of the martingale optimal transport problem on the real line
Probability
2022-06-22 v3
Abstract
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 [Beiglboeck, M., & Juillet, N. (2016). On a problem of optimal transport under marginal martingale constraints. Ann. Probab., 44 (2016), no. 1, 42106] for cost functions of polynomial growth.
Keywords
Cite
@article{arxiv.1905.04574,
title = {Continuity of the martingale optimal transport problem on the real line},
author = {Johannes Wiesel},
journal= {arXiv preprint arXiv:1905.04574},
year = {2022}
}