{
  "id": "1509.01118",
  "version": "v1",
  "published": "2015-09-03T15:04:44.000Z",
  "updated": "2015-09-03T15:04:44.000Z",
  "title": "On viscosity solution of HJB equations with state constraints and reflection control",
  "authors": [
    "Anup Biswas",
    "Hitoshi Ishii",
    "Subhamay Saha",
    "Lin Wang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.OC",
    "math.AP",
    "math.PR"
  ],
  "abstract": "Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in $\\mathbb{R}_+$ with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-03T15:04:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60H30",
      "35J25",
      "49L25"
    ],
    "keywords": [
      "hjb equation",
      "viscosity solution",
      "state constraints",
      "reflection control",
      "value function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901118B"
    }
  }
}