Research On Optimal Reinsurance Of Convex Combination Based On VaR And CTE

Reinsurance is an effective risk management strategy,which plays an important role in the insurance industry.At the beginning of reinsurance,most scholars only considered the insurer,but a reinsurance contract involves both the insurer and the reinsurer,and both parties have conflicting interests.Therefore,in recent years,more and more scholars began to consider the common interests of reinsurance parties.This paper considers the interests of both the original insurer and the reinsurer.Firstly,by introducing the classical literature of reinsurance,this paper introduces three important parts of reinsurance transaction: premium principle,ceded loss function and optimization criterion,and describes them respectively.At the same time,the definitions of VaR and CTE and their basic properties are given.Secondly,under the condition that the loss of the insurer obeys the exponential distribution and the premium principle is the expected value premium principle,the convex combination of VaR of the total loss of the insurer and the reinsurer is taken as the objective function.Through the discussion and analysis of various situations,the theoretical solutions of the optimal proportion coefficient and the optimal retention in the mixed reinsurance are obtained.It provides decision basis for risk management of insurance company.Finally,under the optimization criteria of VaR and CTE,taking the convex combination of VaR and CTE of the total loss of each reinsurance party as the objective function.When the ceded loss function is the specified increasing convex function,the objective function is minimized,and the specific form of the corresponding ceded loss function in the two increasing convex functions is derived.