{
  "id": "1407.0876",
  "version": "v2",
  "published": "2014-07-03T12:04:15.000Z",
  "updated": "2016-06-27T12:19:00.000Z",
  "title": "Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control",
  "authors": [
    "Fulvia Confortola",
    "Marco Fuhrman",
    "Jean Jacod"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/15-AAP1132 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2016, Vol. 26, No. 3, 1743-1773",
  "doi": "10.1214/15-AAP1132",
  "categories": [
    "math.PR"
  ],
  "abstract": "We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition holds (see Assumption (A) below), we prove existence and uniqueness results under Lipschitz conditions on the coefficients. Some counter-examples show that our assumptions are indeed needed. We use a novel approach that allows reduction to a (finite or infinite) system of deterministic differential equations, thus avoiding the use of martingale representation theorems and allowing potential use of standard numerical methods. Finally, we apply the main results to solve an optimal control problem for a marked point process, formulated in a classical way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-03T12:04:15.000Z",
      "title": "Backward stochastic differential equations driven by a marked point process: an elementary approach, with an application to optimal control",
      "abstract": "We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition holds, we prove existence and uniqueness results under Lipschitz conditions on the coefficients. Some counter-examples show that our assumptions are indeed needed. We use a novel approach that allows reduction to a (finite or infinite) system of deterministic differential equations, thus avoiding the use of martingale representation theorems and allowing potential use of standard numerical methods. Finally, we apply the main results to solve an optimal control problem for a marked point process, formulated in a classical way.",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-06-27T12:19:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G55",
      "93E20"
    ],
    "keywords": [
      "backward stochastic differential equations driven",
      "marked point process",
      "optimal control",
      "elementary approach",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0876C"
    }
  }
}