Application of copula in loss reserving

Abstract

Modelling the outstanding claims amount is critical to loss reserving for property-casualty insurers. The dependence between claim size and development time as well as dependence among multiple loss triangles are particularly crucial for an accurate loss reserving process. However, the traditional practice in the insurance industry ignores these dependencies. Hence, there are more and more propositions for using copula methods to model the dependence structure. In this study, we propose an alternative view, differentiating the copula methodology used in modelling reserve for both single line of business and multiple line of business of an insurer. We first examine using an Archimedean copula to model the dependency between claim size and development time. Best fitting distributions for both variables are established and subsequently modeled using a best fitted bivariate Archimedean copula. We then examine a copula regression model for the prediction of unpaid losses for dependent lines of business. This parametric method relates the claim payments in different run-off triangles through a copula function, which allows us to associate the claims among lines of business. For practical application purposes, we consider an insurance portfolio consisting of 2 lines of business: personal and commercial automobile lines. When applied to real data sets from major insurers and compared with the conventional chain ladder method, the copula method of loss reserving for both single and multiple line of businesses yields comparably closer results to the actual outstanding claims.