Dependence Analysis of Insurance Businesses Based on Hierarchical Archimedean Copula Function

Abstract

The dependence between insurance businesses greatly influences the evaluation of insurance companies’ overall reserves. Because of the heterogeneity of risks, the dependence between businesses is often not exactly the same. In order to analyze the asymmetric dependence relationship, an asymmetric dependence structure based on hierarchical Archimedean Copula function is proposed. It is assumed that the loss distribution of business lines follows Log-normal, Gamma and Weibull distribution. And then a hierarchical Copula dependence structure among different businesses is established. By the empirical analysis of the historical data of CPIC’s automobile insurance, transportation insurance, enterprise property insurance and liability insurance, the optimal 4-dim hierarchical Copula structure is selected to analyze the dependence among the four. The empirical results show that automobile insurance and transportation insurance have the strongest dependence, followed by enterprise property insurance and liability insurance. At the same time, based on the obtained hierarchical structure, reserve assessment and risk measurement can be carried out, which provides an insight for analyzing the dependence among multivariate analysis.