{"paper":{"title":"On a problem of optimal transport under marginal martingale constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.PR","authors_text":"Mathias Beiglb\\\"ock, Nicolas Juillet","submitted_at":"2012-08-07T20:03:02Z","abstract_excerpt":"The basic problem of optimal transportation consists in minimizing the expected costs $\\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are fixed. Inspired by recent applications in mathematical finance and connections with the peacock problem, we study this problem under the additional condition that $(X_i)_{i=1,2}$ is a martingale, that is, $\\mathbb {E}[X_2|X_1]=X_1$. We establish a variational principle for this problem which enables us to determine optimal martingale transport plans for specific "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1509","kind":"arxiv","version":2},"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"}