Claims Cost Estimation of Large Insurance Losses

This paper demonstrates our analysis of a liability data set from Royal & SunAlliance. The liability data set is heavy-tailed and the analysis is based on a systematic, unified approach to the estimation of heavy-tailed loss distributions. The method has recently been developed in Royal & SunAlliance and is based on a parametric estimator, the heavy-tailed modified Champernowne distribution, which is corrected with a non-parametric estimator. The correction is obtained by transforming the data set with the estimated modified Champernowne cdf and then estimating the density of the transformed data set by using the classical kernel density estimator. In this paper, we also demonstate a simulation study that calculates the expected cost and the volatility in the liability portfolio, which are fundamental for calculating the premium.