Applying robust scale M-estimators to compute credibility premiums in the large claim case

Viac o knihe

An important aspect of insurance mathematics is the pricing of large claims, which can arise from multiple small claims occurring simultaneously or from single significant events. A key premium calculation principle is the credibility premium, a convex combination of the class mean, reflecting the general behavior of the insurance portfolio, and the individual mean, which considers the specific claim history of the risks involved. The insurer calculating the premium does not need to know the exact claim amount distribution but must make certain assumptions. This thesis examines an insurance portfolio of N risks, where each typically results in small claims, but occasionally large claims occur due to contamination of the small claim distribution. The credibility approach, combined with robust statistics, is applied to separate claim amounts and premiums into ordinary and extreme parts. The ordinary premium is calculated using the credibility principle, assuming the claim distribution follows a Gamma(α,θ₊i) model. Robust estimators are introduced to handle extreme claims, utilizing the mean excess function. The work includes a discussion of robust M-estimators and influence functions, defining two robust scale M-estimators dependent on parameters a and b, and analyzing their optimal values. The thesis concludes with a simulation study assessing the robustness of these estimators against various choices of parameters and sample s