Mixture copulas and insurance applications

Abstract

AbstractIn the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distributionFof the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variableNfollows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property ofFwith respect to both parametersαandλ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.