Modelling dependence in insurance claims process with Lévy copulas (Q2890526)

The authors investigate the potential of Lévy copulas as a tool for modelling dependence between compound Poisson processes. Characteristics are analysed regarding dependence in frequency and dependence in severity allowed by various Lévy copula models. The authors introduce new Lévy copulas, compare them with Clayton Lévy copula and show that Lévy copulas allow for a great range of dependence structures. Procedures for analysing the fit of Lévy copula models are illustrated by fitting a number of Lévy copulas to a set of real data from Swiss workers compensation insurance. A decomposition of trivariate compound Poisson process is provided and ways of modelling dependence by trivariate Lévy copulas are demonstrated.