{
  "id": "1701.08392",
  "version": "v1",
  "published": "2017-01-29T15:56:22.000Z",
  "updated": "2017-01-29T15:56:22.000Z",
  "title": "On optimal control of forward backward stochastic differential equations",
  "authors": [
    "Fouzia Baghery",
    "Nabil Khelfallah",
    "Brahim Mezerdi",
    "Isabelle Turpin"
  ],
  "comment": "15 pages, submitted for publication in Afrika Matematika",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are measure-valued processes, generalizing the usual strict controls. The proof is based on some tightness properties and weak convergence on the space D of c\\`adl\\`ag functions, endowed with the Jakubowsky S-topology. Moreover, under some convexity assumptions, we show that the relaxed optimal control is realized by a strict control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-29T15:56:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60H10",
      "60H30"
    ],
    "keywords": [
      "forward backward stochastic differential equations",
      "optimal control",
      "coupled forward-backward stochastic differential equation",
      "usual strict controls",
      "convexity assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}