Optimal Reinsurance Strategy Based On Two-stage Method

Reinsurance is a common way for insurers to transfer risks in order to reduce their own risks.Obviously,a reinsurance contract involves the interests of both the insurer and the reinsurer.In a reinsurance strategy,Pareto reinsurance can maxi-mize the interests of both parties.That is,one party makes its own interests better while not harming the interests of the other party.Therefore,most of the current literature studies Pareto optimality from the perspective of both insurers and reinsurers.In this paper,based on the value-at-risk(VaR)risk measure and Tail-Value-at-Risk(TVaR)risk measure,the convex functions of VaR and TVaR,which minimize the total loss of insurers and reinsurers,are taken as objective functions respectively.we studies the Pareto-optimal reinsurance strategy for the insurer and the reinsurer by two-stage method.We show that the Pareto-optimal reinsurance policy exists if the reinsurance premiums can be reduced to an integral.Then we take TVaR principle and expectation principle as examples to illustrate the two-stage optimisation procedure by deriving explicitly the Pareto-optimal reinsurance policies.