{
  "id": "1510.08323",
  "version": "v1",
  "published": "2015-10-28T14:40:30.000Z",
  "updated": "2015-10-28T14:40:30.000Z",
  "title": "On the dual problem of utility maximization in incomplete markets",
  "authors": [
    "Lingqi Gu",
    "Yiqing Lin",
    "Junjian Yang"
  ],
  "doi": "10.1016/j.spa.2015.10.009",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-28T14:40:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B28",
      "91B16"
    ],
    "keywords": [
      "incomplete markets",
      "dual problem",
      "bounded random endowment",
      "local martingale",
      "brownian framework"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}