{
  "id": "0711.2834",
  "version": "v1",
  "published": "2007-11-19T03:48:11.000Z",
  "updated": "2007-11-19T03:48:11.000Z",
  "title": "G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty",
  "authors": [
    "Shige Peng"
  ],
  "comment": "Lecture notes, 114 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a new notion of G-normal distributions. This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) through the corresponding G-Brownian motion. We will also present analytical calculations and some new statistical methods with application to risk analysis in finance under volatility uncertainty. Our basic point of view is: sublinear expectation theory is very like its special situation of linear expectation in the classical probability theory. Under a sublinear expectation space we still can introduce the notion of distributions, of random variables, as well as the notions of joint distributions, marginal distributions, etc. A particularly interesting phenomenon in sublinear situations is that a random variable Y is independent to X does not automatically implies that X is independent to Y. Two important theorems have been proved: The law of large number and the central limit theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-19T03:48:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H05",
      "60H30"
    ],
    "keywords": [
      "dynamic risk measure",
      "volatility uncertainty",
      "g-brownian motion",
      "distributions",
      "sublinear expectation theory"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 114,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2834P"
    }
  }
}