A Copula-Based family of Bivariate Composite Models for Claim Severity Modelling

Abstract

In this paper, we consider bivariate composite models for modeling jointly different types of claims and their associated costs in a flexible manner. For expository purposes, the Gumbel copula is paired with the composite Weibull-Inverse Weibull, Paralogistic-Inverse Weibull, and Inverse Burr-Inverse Weibull marginal models. The resulting bivariate copula-based composite models are fitted on motor insurance bodily injury and property damage data from a European motor insurance company and their parameters are estimated via the inference functions for margins method.