On the stability of the martingale optimal transport problem: A set-valued map approach
Ariel Neufeld and
Statistics & Probability Letters, 2021, vol. 176, issue C
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 (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglböck et al. (2021), 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: Martingale optimal transport; Stability; Set-valued map; Berge’s maximum theorem (search for similar items in EconPapers)
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