Clustering of the Kenyan General Insurance Risk Classes by the Archimedean Copula Theory

Abstract

Dependence between risks reduces the benefits of diversification. Modern portfolio theory is based on correlation as a measure of dependence while the criterion presented here is based on the copula theory as a measure of the intrinsic relatedness of different risks classes. The dependencies are examined by fitting copulas, estimating the dependence parameters and lastly using distance matrices to cluster the similar risks together. The study derives its data from the general insurance business in Kenya. The motivation of the study was driven by the fact that insurance companies had collapsed in the past, one reason being the type of business classes they engage in. It is therefore important to understand the dependencies between risks for better risk management. Five major clusters stood out each with peculiar characteristics. The first cluster constituted the lines with a high probability of a huge claim amount: Engineering, Liability, Fire industrial and Theft. The second contains lines with moderate claim amounts as compared to the previous cluster but are rather slightly more frequent: Fire domestic, Personal accident, Workman’s compensation, Motor commercial and motor private. In the following cluster we have the less popular lines under the umbrella of the miscellaneous class. Marine and Transit which is completely erratic clusters singly while the Aviation line whose main business is exported to foreign countries forming the last cluster. This will assist the companies seeking diversification of their risk portfolio and also entry into re-insurance treaties as a criterion for the determination of forwarding proportions is proposed here.

Keywords: Copula, Measures of dependence, Cluster, Distances, Lines of business