{
  "id": "1907.01740",
  "version": "v1",
  "published": "2019-07-01T12:57:49.000Z",
  "updated": "2019-07-01T12:57:49.000Z",
  "title": "Mean-Field Stochastic Linear-Quadratic Optimal Control Problems: Weak Closed-Loop Solvability",
  "authors": [
    "Jingrui Sun",
    "Hanxiao Wang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1806.05215",
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper is concerned with mean-field stochastic linear-quadratic (MF-SLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closed-loop optimal strategy is introduced. It is shown that the open-loop solvability is equivalent to the existence of a weak closed-loop optimal strategy. Moreover, when open-loop optimal controls exist, there is at least one of them admitting a state feedback representation, which is the outcome of a weak closed-loop optimal strategy. Finally, an example is presented to illustrate the procedure for finding weak closed-loop optimal strategies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-01T12:57:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak closed-loop optimal strategy",
      "mean-field stochastic linear-quadratic optimal control",
      "stochastic linear-quadratic optimal control problems",
      "weak closed-loop solvability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}