{
  "id": "2107.08489",
  "version": "v1",
  "published": "2021-07-18T16:48:55.000Z",
  "updated": "2021-07-18T16:48:55.000Z",
  "title": "Stochastic Maximum Principle for Optimal Liquidation with Control-dependent Terminal Time",
  "authors": [
    "Riccardo Cesari",
    "Harry Zheng"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum principle (SMP) which is markedly different in its Hamiltonian condition from that of the standard SMP with fixed terminal time. We present a simple example in which the optimal solution satisfies the SMP in this paper but fails the standard SMP in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-18T16:48:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K45",
      "91G80",
      "93E20"
    ],
    "keywords": [
      "stochastic maximum principle",
      "control-dependent terminal time",
      "fixed terminal time",
      "general optimal liquidation problem",
      "standard smp"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}