Several Reinsurance Strategy Under The Optimal Reinsurance

At present, the study about reinsurance theory has been quite widely, and these references are mostly only consider insurance or reinsurance company unilateral interests, orbased on expected value principle’s optimal reinsurance strategy. With the social development, unilateral consider insurance company or reinsurance company profts have beenincreasingly unrealistic. At present, more and more scholars are trying to looking forthe method which make the proft reached relative maximization. The previous heuristic, frst in a separate consideration on proportional reinsurance, excess loss reinsurancestrategy, based on the insurance company or reinsurance company unilaterally to maximize profts as a staring point, and the resulting in general risk strategy makes both sidesproft achieves relatively the optimal reinsurance strategy. The artical gives the optimalreinsurance models under the proportional reinsurance, excess loss reinsurance strategies,and general risk strategy, and through examples and theorems, the above three kinds ofcircumstances of the optimal reinsurance strategy are introduced in detail.The thesis is divided into four chapters based on the contents:The frst chapter is the introduction. Firstly introduced the research backgoundand the necessity of reinsurance, then given some knowledge of several calssic reinsurance types, such as proportional reinsurance, excess loss reinsurance. Finally, introducedsome kinds of premium principle, including expected value principle, standard deviationprinciple, variance principle, modifed variance principle and exponential principle, andintroduced the related knowledge about retention.The second chapter mainly analyzes the optimal retention under the proportion reinsurance. Through the proportion reinsurance model P （Z≥γ）≥k, in reinsurance company minimal surplus or proft targets have been identifed, and known claim distributionsituation, according to the standard deviation principle, we can get the optimal retentionvalue β.The third chapter mainly analyzes the optimal retention under the excess loss reinsurance. Through the excess loss reinsurance model P （Z≥γ）≥k, in reinsurance companyminimal surplus or proft targets have been identifed, and known claim distribution situation, according to the standard deviation principle, we can get the optimal retentionvalue b. The forth chapter mainly analyzes the optimal reinsurance under the general risk.Considering the standard variance principle, how to make the insurance company andreinsurance company’s general relative risk minimal. Firstly given the general mixed riskreinsurance modelminβEψ1[X R（X） E（X R（X））]+（1β）Eψ2[R（X） E（R（X））],s.t. Π（R）≤P, R₁（x）≤R（x）≤R₂（x）.Then given enough assumptions which makes the reinsurance contract optimal, here,insurance and reinsurance companies can adopt diferent risk strategy. Finally throughseveral theorems and lemmas, we can get the optimal reinsurance strategy under diferentactual conditions and solving the problem.