{
  "id": "1211.1089",
  "version": "v2",
  "published": "2012-11-06T02:09:39.000Z",
  "updated": "2013-11-09T17:19:25.000Z",
  "title": "BSDEs with terminal conditions that have bounded Malliavin derivative",
  "authors": [
    "Patrick Cheridito",
    "Kihun Nam"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show existence and uniqueness of solutions to BSDEs of the form $$ Y_t = \\xi + \\int_t^T f(s,Y_s,Z_s)ds - \\int_t^T Z_s dW_s$$ in the case where the terminal condition $\\xi$ has bounded Malliavin derivative. The driver $f(s,y,z)$ is assumed to be Lipschitz continuous in $y$ but only locally Lipschitz continuous in $z$. In particular, it can grow arbitrarily fast in $z$. If in addition to having bounded Malliavin derivative, $\\xi$ is bounded, the driver needs only be locally Lipschitz continuous in $y$. In the special case where the BSDE is Markovian, we obtain existence and uniqueness results for semilinear parabolic PDEs with non-Lipschitz nonlinearities. We discuss the case where there is no lateral boundary as well as lateral boundary conditions of Dirichlet and Neumann type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-09T17:19:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H10",
      "35K58"
    ],
    "keywords": [
      "bounded malliavin derivative",
      "terminal condition",
      "lateral boundary conditions",
      "locally lipschitz continuous",
      "semilinear parabolic pdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.1089C"
    }
  }
}