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

arXiv: https://arxiv.org/abs/2102.02718 · HTML: https://mlsanity.com/paper/2102.02718/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [A deep learning approach to data-driven model-free pricing and to martingale optimal transport](https://mlsanity.com/paper/2103.11435/) (2021)

## Abstract (arXiv)

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.