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arXiv · 2102.02718

On the stability of the martingale optimal transport problem: A set-valued map approach

Ariel Neufeld·Julian Sester
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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.

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Ariel Neufeld, Julian Sester. 2021-02-04. On the stability of the martingale optimal transport problem: A set-valued map approach. https://arxiv.org/abs/2102.02718

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