{"paper":{"title":"Maximizing functionals of the maximum in the Skorokhod embedding problem and an application to variance swaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Hobson, Martin Klimmek","submitted_at":"2010-12-17T15:38:29Z","abstract_excerpt":"The Az\\'{e}ma-Yor solution (resp., the Perkins solution) of the Skorokhod embedding problem has the property that it maximizes (resp., minimizes) the law of the maximum of the stopped process. We show that these constructions have a wider property in that they also maximize (and minimize) expected values for a more general class of bivariate functions $F(W_{\\tau},S_{\\tau})$ depending on the joint law of the stopped process and the maximum. Moreover, for monotonic functions $g$, they also maximize and minimize $\\mathbb {E}[\\int_0^{\\tau}g(S_t)\\,dt]$ amongst embeddings of $\\mu$, although, perhaps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3909","kind":"arxiv","version":4},"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"}