{"ID":2836362,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.21287","arxiv_id":"2511.21287","title":"Dynamic characterization of barycentric optimal transport problems and their martingale relaxation","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, Beiglböck, Huesmann and Källblad.","short_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 form...","url_abs":"https://arxiv.org/abs/2511.21287","url_pdf":"https://arxiv.org/pdf/2511.21287v1","authors":"[\"Ivan Guo\",\"Severin Nilsson\",\"Johannes Wiesel\"]","published":"2025-11-26T11:28:20Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\",\"q-fin.MF\"]","methods":"[]","has_code":false}