{
  "id": "1706.06824",
  "version": "v1",
  "published": "2017-06-21T11:02:02.000Z",
  "updated": "2017-06-21T11:02:02.000Z",
  "title": "Mild solutions to the dynamic programming equation for stochastic optimal control problems",
  "authors": [
    "Viorel Barbu",
    "Chiara Benazzoli",
    "Luca Di Persio"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show via the nonlinear semigroup theory in $L^1(\\mathbb{R})$ that the $1$-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution $\\varphi\\in C([0,T];W^{1,\\infty}(\\mathbb{R}))$ with $\\varphi_{xx}\\in C([0,T];L^1(\\mathbb{R}))$. The $n$-dimensional case is also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T11:02:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic optimal control problem",
      "dynamic programming equation",
      "nonlinear semigroup theory",
      "unique mild solution",
      "dimensional case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}