Insurance risk capital and risk aggregation: bivariate copula approach

Abstract

This paper discusses the risk aggregation issue in the sphere of the non-life insurance industry. In this context, we attempt to investigate the impact of the dependence structure among losses using copula theory, on the total risk capital estimation measured by the value-at-risk (VaR). First, using numerical illustrations based on a Tunisian insurance company, we apply various copula families that can capture the dependencies across losses that are derived from four lines of business. Then, based on the Monte-Carlo simulation, the total risk capital is deduced by applying VaR on the aggregate loss distributions. We also conduct a comparative analysis between the various types of the copulas. Our findings reveal that there is a regular impact on the capital requirement estimation indicating that a static approach ignoring the real dependencies between different risks can systematically lead to an overestimation of the total capital requirement.