Optimal Design of Default Risk Reinsurance under General Premium Principle

Based on generalized premium principle, the paper studies the optimal reinsurance design with default risk by minimizing VaR measure of the total risk exposure in insurance company. Suppose that the premium principle satisfies the distribution invariance, risk loading and the stop-loss ordering preserving. We obtain the general form of optimal reinsurance strategies, that is, the layer reinsurance strategy. Especially, the expression of optimal reinsurance are provided under the distortion and Dutch premium principles. Finally, two examples are given to illustrate the above methods.