Extreme value theory and copulas: reinsurance in the presence of dependent risks

摘要

An insurer’s ability to accurately estimate the accumulation of risk, particularly in the right hand tail, is vital in ensuring that his risk appetites matches his risk exposures. This paper, therefore, focuses on the modeling of the extremal dependence structure between insurance risks using the Generalized Pareto distribution and the copula technique. The results obtained after comparing the dependence between large losses from two lines of business (motor and fire) of the Nigerian insurance industry and two specific non-life insurance companies, indicates that the correlation coefficients vary and is generally weak. With the aid of the archimedean copula, the analysis makes use of the data pair exhibiting the highest correlation to draw particular attention to the importance of taking into account the extremal dependence structure when quantifying the risk capital, allocating risk and when estimating the net reinsurance premium under different reinsurance strategies.