{
  "id": "1804.04911",
  "version": "v1",
  "published": "2018-04-13T12:18:31.000Z",
  "updated": "2018-04-13T12:18:31.000Z",
  "title": "A Mean Field Game of Optimal Portfolio Liquidation *",
  "authors": [
    "Guanxing Fu",
    "Paulwin Graewe",
    "Ulrich Horst",
    "Alexandre Popier"
  ],
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a FBSDE with possibly singular terminal condition on the backward component or, equivalently, in terms of a FBSDE with finite terminal value, yet singular driver. Extending the method of continuation to linear-quadratic FBSDE with singular driver we prove that the MFG has a unique solution. Our existence and uniqueness result allows to prove that the MFG with possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T12:18:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field game",
      "optimal portfolio liquidation",
      "possibly singular terminal condition",
      "finite terminal value",
      "singular driver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}