{"ID":2847605,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27451","arxiv_id":"2510.27451","title":"Bi-martingale optimal transport and its applications","abstract":"We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale framework underlies and interconnects several variational problems on the space of probability measures. For the quadratic cost, it provides an optimal transport interpretation of the second Zolotarev distance on $\\mathrm{P}_2(\\mathbb{R}^d)$. For a broader class of convex costs, it leads to optimization problems under convex order constraints, encompassing in particular the Zolotarev projection onto the cone of dominating probability measures. As a main application, we construct a $Γ$-convergent bi-martingale approximation of the classical martingale optimal transport problem. This scheme robustly accommodates deviations from convex order between the marginal distributions and overcomes the well-known instability of MOT with respect to variations of the marginals in higher dimensions.","short_abstract":"We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale framework underlies and interconnects several variational problems on the space...","url_abs":"https://arxiv.org/abs/2510.27451","url_pdf":"https://arxiv.org/pdf/2510.27451v1","authors":"[\"Karol Bołbotowski\"]","published":"2025-10-31T13:00:38Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[]","has_code":false}