Modelling Dependence in Insurance Claims Processes with Lévy Copulas

Abstract

In this paper we investigate the potential of Levy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Levy copula models. Through the introduction of new Levy copulas and comparison with the Clayton Levy copula, we show that Levy copulas allow for a great range of dependence structures.Procedures for analysing the fit of Levy copula models are illustrated by fitting a number of Levy copulas to a set of real data from Swiss workers compensation insurance. How to assess the fit of these models with respect to the dependence structure exhibited by the dataset is also discussed.Finally, we provide a decomposition of the trivariate compound Poisson process and discuss how trivariate Levy copulas model dependence in this multivariate setting.