{
  "id": "1106.3273",
  "version": "v2",
  "published": "2011-06-16T17:00:11.000Z",
  "updated": "2012-05-07T14:43:45.000Z",
  "title": "A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations",
  "authors": [
    "Marcel Nutz"
  ],
  "comment": "27 pages",
  "journal": "Electronic Journal of Probability, Vol. 17, No. 23, pp. 1-23, 2012",
  "doi": "10.1214/EJP.v17-1892",
  "categories": [
    "math.PR",
    "cs.SY",
    "math.OC",
    "q-fin.RM"
  ],
  "abstract": "We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen as a non-Markovian analogue of the Hamilton-Jacobi-Bellman partial differential equation. Moreover, our value process yields a generalization of the G-expectation to the context of SDEs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-07T14:43:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "49L20",
      "60H10",
      "60G44",
      "91B30"
    ],
    "keywords": [
      "non-markovian stochastic differential equations",
      "quasi-sure approach",
      "study stochastic differential equations",
      "hamilton-jacobi-bellman partial differential equation",
      "second order backward sde"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3273N"
    }
  }
}