{
  "id": "2012.13683",
  "version": "v1",
  "published": "2020-12-26T06:47:29.000Z",
  "updated": "2020-12-26T06:47:29.000Z",
  "title": "Non-Equivalence of Stochastic Optimal Control Problems with Open and Closed Loop Controls",
  "authors": [
    "Jiongmin Yong",
    "Jianfeng Zhang"
  ],
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "For an optimal control problem of an It\\^o's type stochastic differential equation, the control process could be taken as open-loop or closed-loop forms. In the standard literature, provided appropriate regularity, the value functions under these two types of controls are equal and are the unique (viscosity) solution to the corresponding (path-dependent) HJB equation. In this short note, we show that these value functions can be different in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-26T06:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "49L25"
    ],
    "keywords": [
      "stochastic optimal control problems",
      "closed loop controls",
      "non-equivalence",
      "type stochastic differential equation",
      "value functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}