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

Continuity of the value martingale optimal transport problem on real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) Wiesel (2019). We present a new perspective this result using theory set-valued maps. In particular, results from Beiglböck et al. (2021), we show that set measures with fixed is continuous, i.e., lower- upper hemicontinuous, marginals. Moreover, establish compactness optimizers as well hemicontinuity