{
  "id": "2208.06535",
  "version": "v1",
  "published": "2022-08-13T00:17:01.000Z",
  "updated": "2022-08-13T00:17:01.000Z",
  "title": "$g$-Expectation of Distributions",
  "authors": [
    "Mingyu Xu",
    "Zuo Quan Xu",
    "Xun Yu Zhou"
  ],
  "categories": [
    "math.PR",
    "math.OC",
    "q-fin.MF",
    "q-fin.RM"
  ],
  "abstract": "We define $g$-expectation of a distribution as the infimum of the $g$-expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear $g$ where the $g$-expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant $g$-expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-13T00:17:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expectation",
      "distribution",
      "financial dynamic portfolio choice",
      "special cases",
      "terminal random variables sharing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}