The Optimal Retention For A Reinsurance Under The Variance Related And Wang Premium Principels

This paper introduces the definition of reinsurance, the common reinsurance premium principles and risk measures. We pick up the stop-loss reinsurance to be our object. Under the VaR and CTE risk measures, we solved the analytical expressions of optimal retentions with three premium principles. In addition, we refer the idea of p-average value to improved the Wang risk measures. After that,we transform different distortion functions to have new Wang premium principles and p-mean Wang premium principles. With the new premium principles, we can work out the algebraic equation of the optimal reinsurance retentions.With the improved Wang risk measures, we can export the Conditional-Wang premium principles because of the different distortion functions which we have given.Under the new p-mean Wang premium principles, through the example, we can find out something different about the existence of optimal retentions. Compared with the results, the existence of the solutions for optimal retentions under Wang premium principles is more than that under p-mean Wang premium principles.In the end, the existence of the solution for optimal retention under three Variance related premium principles with different premium additional factors is compared by the numerical simulation. The following result is obtained: CTE is superior to VaR for the existence of retention under three kinds of variance related premium principles.