High level quantile approximations of sums of risks

A. Cuberos; E. Masiello; V. Maume-Deschamps

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 141-158, electronic only
  • ISSN: 2300-2298

Abstract

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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.

How to cite

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A. Cuberos, E. Masiello, and V. Maume-Deschamps. "High level quantile approximations of sums of risks." Dependence Modeling 3.1 (2015): 141-158, electronic only. <http://eudml.org/doc/275860>.

@article{A2015,
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.},
author = {A. Cuberos, E. Masiello, V. Maume-Deschamps},
journal = {Dependence Modeling},
keywords = {regularly varying functions; value at risk estimation; risk aggregation},
language = {eng},
number = {1},
pages = {141-158, electronic only},
title = {High level quantile approximations of sums of risks},
url = {http://eudml.org/doc/275860},
volume = {3},
year = {2015},
}

TY - JOUR
AU - A. Cuberos
AU - E. Masiello
AU - V. Maume-Deschamps
TI - High level quantile approximations of sums of risks
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 141
EP - 158, electronic only
AB - 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.
LA - eng
KW - regularly varying functions; value at risk estimation; risk aggregation
UR - http://eudml.org/doc/275860
ER -

References

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