{
  "id": "1205.5140",
  "version": "v1",
  "published": "2012-05-23T09:57:52.000Z",
  "updated": "2012-05-23T09:57:52.000Z",
  "title": "Backward stochastic differential equations and optimal control of marked point processes",
  "authors": [
    "Fulvia Confortola",
    "Marco Fuhrman"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution on the data. We next address optimal control problems for point processes of general non-markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function. Finally we introduce a Hamilton-Jacobi-Bellman equation, also stochastic and of backward type, for this class of control problems: when the state space is finite or countable we show that it admits a unique solution which identifies the (random) value function and can be represented by means of the BSDEs introduced above.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-23T09:57:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60H10"
    ],
    "keywords": [
      "backward stochastic differential equations",
      "marked point processes",
      "address optimal control problems",
      "value function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5140C"
    }
  }
}