Dynamic characterization of barycentric optimal transport problems and their martingale relaxation

Ivan Guo, Severin Nilsson and Johannes Wiesel

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Abstract: We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale relaxation of this problem, and relate it to the martingale Benamou-Brenier formula of Backhoff-Veraguas, Beiglb\"ock, Huesmann and K\"allblad.

Date: 2025-11
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