{
  "id": "0909.3335",
  "version": "v1",
  "published": "2009-09-17T22:36:25.000Z",
  "updated": "2009-09-17T22:36:25.000Z",
  "title": "Efficient calculation of risk measures by importance sampling -- the heavy tailed case",
  "authors": [
    "Henrik Hult",
    "Jens Svensson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms, designed for efficient tail probability estimation, can significantly improve Monte Carlo estimators of tail-based risk measures. In the heavy-tailed setting, when the random variable of interest has a regularly varying distribution, we provide sufficient conditions for the asymptotic relative error of importance sampling estimators of risk measures, such as Value-at-Risk and expected shortfall, to be small. The results are illustrated by some numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-17T22:36:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60F05"
    ],
    "keywords": [
      "importance sampling",
      "heavy tailed case",
      "efficient calculation",
      "tail-based risk measures",
      "standard monte carlo simulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3335H"
    }
  }
}