{
  "id": "1110.1588",
  "version": "v1",
  "published": "2011-10-07T17:15:05.000Z",
  "updated": "2011-10-07T17:15:05.000Z",
  "title": "Regularity Properties of Viscosity Solutions of Integro-Partial Differential Equations of Hamilton-Jacobi-Bellman Type",
  "authors": [
    "Shuai Jing"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math.AP",
    "math.OC"
  ],
  "abstract": "We study the regularity properties of integro-partial differential equations of Hamilton-Jocobi-Bellman type with terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a Brownian motion and a compensated Poisson random measure. More precisely, we prove that, under appropriate assumptions, the viscosity solution of such equations is jointly Lipschitz and jointly semiconcave in $(t,x)\\in\\Delta\\times\\R^d$, for all compact time intervals $\\Delta$ excluding the terminal time. Our approach is based on the time change for the Brownian motion and on Kulik's transformation for the Poisson random measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-07T17:15:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10",
      "60H30",
      "93E20"
    ],
    "keywords": [
      "integro-partial differential equations",
      "regularity properties",
      "viscosity solution",
      "hamilton-jacobi-bellman type",
      "brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1588J"
    }
  }
}