{
  "id": "1110.1564",
  "version": "v1",
  "published": "2011-10-07T15:16:41.000Z",
  "updated": "2011-10-07T15:16:41.000Z",
  "title": "A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations",
  "authors": [
    "Jiongmin Yong"
  ],
  "comment": "27 pages",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained, which are uniquely solvable under certain conditions. Then a feedback representation is obtained for the optimal control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-07T15:16:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N10",
      "49N35",
      "93E20"
    ],
    "keywords": [
      "mean-field stochastic differential equations",
      "linear-quadratic optimal control problem",
      "mean-field forward-backward stochastic differential",
      "forward-backward stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1564Y"
    }
  }
}