Comparison of Single and Composite Distributions in Modelling Auto Mobile Insurance Losses for Risk Measure Estimation

Abstract

Estimating risk associated with taking on random losses among various insurance policies is crucial, as it aids in obtaining the right balance between the reserve amount for paying indemnities and capital for investment to attract gains necessary to keep an insurance company in business. Fitting the right probabilistic distribution to insurance claims data is the first step in obtaining a good risk estimate for claim losses due to the complicated nature of claims data. Literature has shown that single distributions are incapable of holistically capturing the differences in claim losses due to the varying nature of small and large claims. Composite distributions, on the other hand, have shown tremendous promise in capturing the underlying dynamics that exist in claims data over some dispensations. To that end, in estimating risk measures associated with insurance losses in Ghana, this study first employs single distributions and then composite distributions to describe automobile insurance losses in Ghana for comparison. Two hundred and forty (240) composite distributions were fitted, and the top five were selected and presented taking into consideration the goodness of fit criterion: AIC, BIC, and Log-likelihood. Estimates of the composite distribution are computed using both numerical maximum likelihood estimation and general-purpose optimizers and numerical optimization techniques. The 16 single distributions that were combined to form the composite distributions were also separately fitted. For each of the top five selected single and composite distributions, Value at Risk (VaR) and Tail Value at Risk (TVaR) are estimated at 95% and 99% security levels. A comparison of the single and composite distributions showed that the composite distribution fitted better compared to the single distribution.