On the stability of the martingale optimal transport problem: A set-valued map approach
Probability
2021-04-23 v2 Optimization and Control
Mathematical Finance
Abstract
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglb\"ock, Jourdain, Margheriti, and Pammer [5], we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals.
Keywords
Cite
@article{arxiv.2102.02718,
title = {On the stability of the martingale optimal transport problem: A set-valued map approach},
author = {Ariel Neufeld and Julian Sester},
journal= {arXiv preprint arXiv:2102.02718},
year = {2021}
}