{
  "id": "1705.04299",
  "version": "v1",
  "published": "2017-05-11T17:34:26.000Z",
  "updated": "2017-05-11T17:34:26.000Z",
  "title": "Maximum principle for a stochastic delayed system involving terminal state constraints",
  "authors": [
    "Jiaqiang Wen",
    "Yufeng Shi"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-11T17:34:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60H10"
    ],
    "keywords": [
      "terminal state constraints",
      "stochastic delayed system",
      "maximum principle",
      "stochastic delayed linear-quadratic control",
      "backward stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}