CTE Criteria For Optimal Quota-share And Stop-loss Reinsurance From The Perspectives Of Insurer And Reinsurer

It is well known that reinsurance is an effective measure for risk management and it plays a critical role in the insurance activities.Tan et al.[9]considers the optimal reinsurance problem from the perspective of the insurer from the perspective of VaR and CTE risk measurement.However,the insurer and the reinsurer have conflicting interests.The reinsurance contract is the best to the insurer but it may be not the best to the reinsurer,so it is necessary to consider the interests of both the insurer and the reinsurer.In this paper,we extend the results proposed by Tan et al.[9],taking into account The optimization problem of convex combination of the insurer and the rein-surer.More concretely,for the two reinsurance models of quota-share reinsurance and stop-loss reinsurance,we combine the risk of the insurer and the reinsurer to a convex combination,and use the CTE risk measure to obtain the minimum of the risk after the convex combination.In this paper,We use 16 kinds of common premium principles to optimize the above problems.The results show that the existence of the nontrivial optimal solutions for the quota-share reinsurance and the stop loss reinsurance is not only related to the premium principle that we choose,but also to the coefficient of the convex combination.The second chapter introduces the background and definition of VaR and CTE,and draws some basic conclusions about VaR and CTE.In the third chapter and the fourth chapter,we discuss the quota-share reinsurance and the stop-loss reinsurance respectively.We study the simple properties of the quota-share reinsurance and the stop-loss reinsurance,and get the sufficient and necessary conditions for the optimal nontrivial solution corresponding to the quota-share reinsurance and the suffi-cient conditions for the optimal nontrivial solution for the stop-loss reinsurance.In the fifth chapter,we give some specific examples and derive the form of the corresponding optimal solution,and compare the results with the conclusions obtained from Tan et al.[9]and H Liu and Y Fang[13].