Reinsurance Pricing of Large Motor Insurance Claims in Nigeria: An Extreme Value Analysis

Insurers that undertake high risk profiles usually exceed their financial capabilities, hence the importance of reinsurance. This allows the insurance company to cover risks that they, under normal circumstances, would not be able to cover on their own. An insurer needs to be able to evaluate his solvency probability and consequently, adjust his retention levels appropriately because the insurer's retention level plays a vital role in determining the premiums he will pay to the reinsurer. To illustrate how Extreme Value theory can be applied, this study delves into modeling the probabilistic behavior of the frequency and severity of large motor claims from the Nigerian insurance sector (2013-2016) using the Negative Binomial-Generalized Pareto distribution (NB-GPD). The annual loss distribution is simulated using the Monte Carlo method. Pricing of the Excess-of-loss (XL) reinsurance is also examined to aid insurers in optimizing their risk management decision in regards to the choice of their risk transfer position.