{
  "id": "1306.3631",
  "version": "v5",
  "published": "2013-06-16T07:07:29.000Z",
  "updated": "2015-11-09T19:27:23.000Z",
  "title": "Viscosity solutions of obstacle problems for Fully nonlinear path-dependent PDEs",
  "authors": [
    "Ibrahim Ekren"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in $(t,\\omega)$, and generator Lipschitz continuous in $(y,z,\\gamma)$. We prove that our definition of viscosity solutions is consistent with the classical solutions, and satisfy a stability result. We show that the value functional defined via the second order reflected backward stochastic differential equation is the unique viscosity solution of the variational inequalities.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-29T16:33:32.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-11-09T19:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D40",
      "35K10",
      "60H10",
      "60H30"
    ],
    "keywords": [
      "fully nonlinear path-dependent pdes",
      "viscosity solution",
      "obstacle problem",
      "backward stochastic differential equation",
      "order reflected backward stochastic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3631E"
    }
  }
}