Modelling large claims in order to optimise the reinsurance program

Abstract

Reinsurance is one of the cornerstones in the actuarial mathematics. When the company deals with large claims, the matter of choosing the optimal reinsurance strategy becomes especially important as it helps to reduce the risks of the insurance company. For defining the best reinsurance program, the insurer needs to know the behaviour of large claims in portfolio. Based on historical data of incurred claims, it is possible to estimate the ultimate values with chain ladder method. The most common claim distributions are used to fit to the ultimate amounts and the best distribution is chosen for generating claim severities. Based on generated number of claims and claim sizes, it’s possible to simulate many scenarios for calculating the total loss without reinsurance and net losses after reinsurance. In case of excess of loss reinsurance, the reinsurer covers the part of claim which exceeds the retention level. Comparing net losses from all reinsurance programs, the insurance company can make a decision whether the reinsurance program is beneficial depending on the premium which the reinsurance company requests.