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High level quantile approximations of sums of risks

Author

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  • Cuberos A.

    (Université de Lyon, Université Lyon 1, Laboratoire SAF EA 2429, SCOR SE)

  • Masiello E.

    (Université de Lyon, Université Lyon 1, Institut Camille Jordan ICJ UMR 5208 CNRS)

  • Maume-Deschamps V.

    (Université de Lyon, Université Lyon 1, Institut Camille Jordan ICJ UMR 5208 CNRS)

Abstract

The approximation of a high level quantile or of the expectation over a high quantile (Value at Risk (VaR) or Tail Value at Risk (TVaR) in risk management) is crucial for the insurance industry.We propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We show that using the distribution of the maximum to approximate the VaR is much better than using the marginal. Our method seems to work well in high dimension (100 and higher) and gives good results when approximating the VaR or TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed.

Suggested Citation

  • Cuberos A. & Masiello E. & Maume-Deschamps V., 2015. "High level quantile approximations of sums of risks," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, October.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:18:n:10
    DOI: 10.1515/demo-2015-0010
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    References listed on IDEAS

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