{
  "id": "1201.6614",
  "version": "v1",
  "published": "2012-01-31T16:52:48.000Z",
  "updated": "2012-01-31T16:52:48.000Z",
  "title": "Backward Stochastic Differential Equations and Feynman-Kac Formula for Multidimensional Lévy Processes, with Applications in Finance",
  "authors": [
    "Jianzhong Lin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L\\'{e}vy process with moments of all orders. The results are important from a pure mathematical point of view as well as in the world of finance: an application to Clark-Ocone and Feynman-Kac formulas for multidimensional L\\'{e}vy processes is presented. Moreover, the Feynman-Kac formula and the related partial differential integral equations provide an analogue of the famous Black-Scholes partial differential equation and thus can be used for the purpose of option pricing in a multidimensional L\\'{e}vy market.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-31T16:52:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H15",
      "60G55"
    ],
    "keywords": [
      "backward stochastic differential equations",
      "feynman-kac formula",
      "multidimensional lévy processes",
      "partial differential integral equations",
      "black-scholes partial differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.6614L"
    }
  }
}