{
  "id": "1412.8495",
  "version": "v1",
  "published": "2014-12-29T22:05:17.000Z",
  "updated": "2014-12-29T22:05:17.000Z",
  "title": "Viscosity Solutions of Path-dependent Integro-differential Equations",
  "authors": [
    "Christian Keller"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. [Ann. Probab. 42 (2014), no. 1, 204-236] to path-dependent integro-differential equations and establish well-posedness, i.e., existence, uniqueness, and stability, for a class of semilinear path-dependent integro-differential equations with uniformly continuous data. Closely related are non-Markovian backward SDEs with jumps, which provide a probabilistic representation for solutions of our equations. The results are potentially useful for applications using non-Markovian jump-diffusion models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-29T22:05:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45K05",
      "35D40",
      "60H10",
      "60H30"
    ],
    "keywords": [
      "viscosity solutions",
      "semilinear path-dependent integro-differential equations",
      "non-markovian jump-diffusion models",
      "path-dependent pdes",
      "non-markovian backward sdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}