{
  "id": "1908.09208",
  "version": "v1",
  "published": "2019-08-24T21:02:09.000Z",
  "updated": "2019-08-24T21:02:09.000Z",
  "title": "The Wellposedness of Path-dependent Multidimensional Forward-backward SDE",
  "authors": [
    "Kaitong Hu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study in this paper the wellposedness of path-dependent multidimensional forward-backward SDE. By path-dependent we mean that the coefficients of the forward-backward SDE at time t can depend on the whole path of the forward process up to time t. These kinds of forward-backward SDE appear when solving path-dependent stochastic control problem by means of variational calculus. At the heart of our analysis is the construction of a decoupling random field on the path space. Finally, we show that the solution of a path-dependent forward-backward SDE is stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-24T21:02:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H30",
      "35R60",
      "34F05"
    ],
    "keywords": [
      "path-dependent multidimensional forward-backward sde",
      "wellposedness",
      "solving path-dependent stochastic control problem",
      "path-dependent forward-backward sde",
      "sde appear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}