{"paper":{"title":"Improved Fr\\'echet$-$Hoeffding bounds on $d$-copulas and applications in model-free finance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"math.PR","authors_text":"Antonis Papapantoleon, Thibaut Lux","submitted_at":"2016-02-29T10:28:08Z","abstract_excerpt":"We derive upper and lower bounds on the expectation of $f(\\mathbf{S})$ under dependence uncertainty, i.e. when the marginal distributions of the random vector $\\mathbf{S}=(S_1,\\dots,S_d)$ are known but their dependence structure is partially unknown. We solve the problem by providing improved \\FH bounds on the copula of $\\mathbf{S}$ that account for additional information. In particular, we derive bounds when the values of the copula are given on a compact subset of $[0,1]^d$, the value of a functional of the copula is prescribed or different types of information are available on the lower dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08894","kind":"arxiv","version":5},"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"}