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High level quantile approximations of sums of risks

High level quantile approximations of sums of risks AbstractThe 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 newmethod to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio betweenthe VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We show that using thedistribution of the maximum to approximate the VaR is much better than using the marginal. Our methodseems to work well in high dimension (100 and higher) and gives good results when approximating the VaRor TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

High level quantile approximations of sums of risks

Dependence Modeling , Volume 3 (1): 1 – Oct 16, 2015

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Publisher
de Gruyter
Copyright
© 2015 A. Cuberos et al.
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2015-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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 newmethod to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio betweenthe VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We show that using thedistribution of the maximum to approximate the VaR is much better than using the marginal. Our methodseems to work well in high dimension (100 and higher) and gives good results when approximating the VaRor TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed.

Journal

Dependence Modelingde Gruyter

Published: Oct 16, 2015

References