{
  "id": "1310.6943",
  "version": "v1",
  "published": "2013-10-25T14:50:19.000Z",
  "updated": "2013-10-25T14:50:19.000Z",
  "title": "Dual and backward SDE representation for optimal control of non-Markovian SDEs",
  "authors": [
    "Marco Fuhrman",
    "Huyên Pham"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity assumption on the SDE. We develop a controls randomization approach, and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with nonpositive jumps under a single probability measure, which can be viewed as a path-dependent version of the Hamilton-Jacobi-Bellman equation, and an extension to $G$ expectation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-25T14:50:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward sde representation",
      "optimal control",
      "non-markovian sdes",
      "study optimal stochastic control problem",
      "non-markovian stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6943F"
    }
  }
}