Optimal reinsurance contracts under the reinsurer’s risk constraint with VaR risk measures

Abstract

Most researchers in insurance field have not been considering the reinsurer’s risk. Theoretically, the quantity of reinsurer’s risk is not limited. However, in the real-world insurance industry, reinsurer always put a limit on coverage, otherwise the reinsurer will experience a heavy financial burden when the insurer bears an unexpected large loss. In this paper, we review the optimal reinsurance problem under VaR risk measures framework when the limitation for reinsurer’s risk exposure are limited by a constant. By analyzing the VaR of the insurer’s total risk exposure, optimality can be fulfilled and end up in obtaining the expected reinsurance policy. Through the study, it is reveal that the stop-loss reinsurance with a policy limit is constantly the optimal reinsurance policy under VaR risk measures. Determination of optimal quantity of ceded risk depends on the confidence level, the safety loading and the limitation of the constant. A numerical analysis on company claims data is carried out in order to find the optimal ceded loss function.