Loss and allocated Loss adjustment expenses modelling using symmetric and asymmetric copulas.

Abstract

When a claim report is filed by an insurer, the claim amount is recorded as LOSS and allocated loss adjustment expense (ALAE) is incurred to verify and settle the claim. The knowledge of the relationship between these two variables is crucial for pricing reinsurance premiums. While a mathematical tool called the Archimedean family of copulas, which are mostly symmetric copulas, has been commonly used to model LOSS-ALAE relationship, recent findings have suggested the potential use of asymmetric copulas in modelling this relationship to account for the upper tail dependency commonly found in LOSS-ALAE data.

In this research, asymmetrical extreme value copulas are used to model the dependencies in addition to Archimedean copulas. Findings show that asymmetrical extreme value copulas Galambos and Gumbel provided a better fit as compared to conventional Archimedean Copula. This result is also substantiated with a pure premium analysis for reinsurance treaties.