{
  "id": "1804.09918",
  "version": "v1",
  "published": "2018-04-26T07:27:30.000Z",
  "updated": "2018-04-26T07:27:30.000Z",
  "title": "Mean-Field Stochastic Control with Elephant Memory in Finite and Infinite Time Horizon",
  "authors": [
    "Nacira Agram",
    "Bernt Øksendal"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Our purpose of this paper is to study stochastic control problem for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history in both cases, finite and infinite time horizon. - In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem. - For infinite horizon, we derive sufficient and necessary maximum principles. As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-26T07:27:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H20",
      "60J75",
      "93E20",
      "91G80",
      "91B70"
    ],
    "keywords": [
      "infinite time horizon",
      "mean-field stochastic control",
      "elephant memory",
      "mean-field linear quadratic control problem",
      "study stochastic control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}