High level quantile approximations of sums of risks.

Summary 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 use results on consistently varying functions. We compare the efficiency of our method with classical ones, on several models. Our method 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.