{"paper":{"title":"An Explicit Martingale Version of Brenier's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.CP","authors_text":"Nizar Touzi (CMAP), Pierre Henry-Labordere (SOCIETE Generale)","submitted_at":"2013-02-20T09:50:06Z","abstract_excerpt":"By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \\cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions corresponding to the lower and upper bounds. These explicit extremal probability measures coincide with the unique left and right monotone martingale tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4854","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}