Dependence Modelling for Heavy-Tailed Multi-Peril Insurance Losses

Abstract

The Danish fire loss dataset records commercial fire losses under three insurance coverages: building, contents, and profits. Existing research has primarily focused on the heavy-tail behaviour of the losses but ignored the relationship among different insurance coverages. In this paper, we aim to model the aggregate loss for all three coverages. To study the pairwise dependence of claims from all types of coverage, an independent model, a hierarchical model, and some copula-based models are proposed for the frequency component. Meanwhile, we applied composite distributions to capture the heavy-tailed severity component. It is shown that consideration of dependence for the multi-peril frequencies (i) significantly enhances model goodness-of-fit and (ii) provides more accurate risk measures of the aggregated losses for all types of coverage in total.

Keywords

• dependence modelling
• ratemaking
• multi-peril insurance
• heavy-tail distributions
• composite models
• copulas