Selection of Claim Size Distribution in General Insurance

Abstract

Computations in general insurance are often based on models such as the collective risk model, which uses a compound distribution to describe the aggregated losses. A critical part of this model is the un- certainty of claim sizes. The claim sizes are typically modeled through simple two-parameter distributions where their fit are assessed by Q- Q plots. Another approach is to use more flexible distributions which can be fitted to different samples, everything between light-tailed and heavy-tailed distributions. We will use an extended Pareto model with three parameters and a 4-parameter model with some of the standard two-parameter families as special cases. We use Monte Carlo-simulations to analyze how well the 3- and 4-parameter models estimate the reserve compared to the special cases Gamma, Weibull and Pareto distribution. More param- eters provide a more flexible model, but it also means that the uncer- tainty becomes larger in the reserve estimate. We use error analysis to determine how well the models performs for the different distribu- tions and for varying sample sizes. Finally, we find that the 3- and 4-parameter models provide a good fit for sample sizes n = 5 000 and n = 500, and partly for n = 50. We find that the 4-parameter model is superior to the 3-parameter model. Also, the 4-parameter model is slightly overestimating the reserve which makes the 4-parameter model a safe and conservative choice for the claim size distribution.