{
  "id": "1111.1851",
  "version": "v2",
  "published": "2011-11-08T10:08:16.000Z",
  "updated": "2012-09-20T20:07:16.000Z",
  "title": "Random variables as pathwise integrals with respect to fractional Brownian motion",
  "authors": [
    "Yuliya Mishura",
    "Georgiy Shevchenko",
    "Esko Valkeila"
  ],
  "journal": "Stochastic Processes Appl. 123 (2013), 2353-2369",
  "doi": "10.1016/j.spa.2013.02.015",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-20T20:07:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60H05",
      "60G15",
      "91G10"
    ],
    "keywords": [
      "fractional brownian motion",
      "random variable",
      "pathwise integrals",
      "fractional black-scholes model",
      "pathwise stochastic integral"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1851M"
    }
  }
}