{"paper":{"title":"On the dual problem of utility maximization in incomplete markets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Junjian Yang, Lingqi Gu, Yiqing Lin","submitted_at":"2015-10-28T14:40:30Z","abstract_excerpt":"In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in the paper of Cvitani\\'{c}-Schachermayer-Wang (2001) and prove the following statement: in the Brownian framework, the countably additive part $Q^r$ of the dual optimizer $Q\\in (L^\\infty)^*$ obtained in that paper can be represented by the terminal value of a supermartingale deflator $Y$ defined in the paper of Kramkov-Schachermayer (1999), which is a local martingale."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08323","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"}