{
  "id": "1806.01166",
  "version": "v1",
  "published": "2018-06-04T16:05:20.000Z",
  "updated": "2018-06-04T16:05:20.000Z",
  "title": "Risk measures with markets volatility",
  "authors": [
    "Fei Sun",
    "Yijun Hu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we will study some risk measures with markets volatility. These risk measures are defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space. This space is denoted by $L^{p(\\cdot)}$ where the variable exponent $p(\\cdot)$ is no longer a given real number like the space $L^{p}$, but a random variable, which reflects the possible volatility of the financial markets. This space was studied in detail by Cheng and Xu (2013) and we will defined several well-known risk measures on it. The dual representations for them are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-04T16:05:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91B30",
      "91B32",
      "46E30"
    ],
    "keywords": [
      "markets volatility",
      "variable exponent bochner-lebesgue space",
      "well-known risk measures",
      "financial positions",
      "financial markets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}