Focussed selection of the claim severity distribution

Risk assessment is a core theme within non-life insurance and estimation of quantiles far out in the upper tail is therefore one of the main applications of the total loss distribution of a non-life insurance portfolio. The choice of claim severity distribution should therefore reflect this. Therefore, we have explored how the focussed information criterion, FIC, aimed at finding the best model for estimating a given parameter of interest, the focus parameter, works as a tool for selecting the claim size distribution. As a quantile cannot be used directly as a focus parameter, we have tried different proxy focus parameters. To see how the FIC performs in this setting, compared to the other commonly used model selection methods AIC and BIC, we have performed a simulation study. In particular, we wanted to investigate the effect of the heaviness of the tail of the claim size distribution and the amount of available data. The performance of the different model selection methods was then evaluated based on the quality of the resulting estimates of the quantiles. Our study shows the best of the focussed criteria is the FIC $ _{\epsilon } $ ϵ, based on one single quantile from the claim severity distribution. Further, the performance of the FIC $ _{\epsilon } $ ϵ is mostly either comparable to or considerably better than that of the BIC, which is the best performing of the state of the art approaches. In particular, the FIC $ _{\epsilon } $ ϵ works well when the data are heavy-tailed, when the sample size is rather low and when the parameter of interest is the quantile far out in the tail of the total loss distribution.