{
  "id": "1402.6793",
  "version": "v3",
  "published": "2014-02-27T06:11:14.000Z",
  "updated": "2014-04-17T10:46:08.000Z",
  "title": "A Stochastic Maximum Principle for Processes Driven by G-Brownian Motion and Applications to Finance",
  "authors": [
    "Zhongyang Sun",
    "Xin Zhang",
    "Junyi Guo"
  ],
  "comment": "This paper has been withdraw by the author due to some minor error on the application of G-BSDE theory",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion introduced by Peng(2007). Based on the theory of stochastic differential equations on a sublinear expectation space $(\\Omega,\\mathcal{H},\\hat{\\mathbb{E}})$, we prove a stochastic maximum principle for controlled processes driven by G-Brownian motion. Then we obtain the maximum condition in terms of the $\\mathcal{H}$-function plus some convexity conditions constitute sufficient conditions for optimality. Finally, we solve a portfolio optimization problem with ambiguous volatility as an explicitly illustrated example of the main result.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-17T10:46:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60H10"
    ],
    "keywords": [
      "stochastic maximum principle",
      "processes driven",
      "g-brownian motion",
      "convexity conditions constitute sufficient conditions",
      "stochastic optimal control problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6793S"
    }
  }
}