Optimal Quota-share And Stop-loss Reinsurance Based On The Viewpoint Of The Insurer And The Reinsurer

Reinsurance is the act of insurer to transfer risks and responsibilities from other insurers by signing a sub contract under the original insurance contracts.It is an effective risk management tool for the insurer to control losses.There is no doubt that it plays a stabilizing and boosting role for the whole insurance industry,and is conducive to maintaining market harmony.Then it is necessary for the insurer to carry out the risk transfer through reinsurance when he faces the huge risk.The most important part of the reinsurance problem is the optimization problem.At present,there are many literatures to study the optimal reinsurance from the point of view of the insurer.But the optimal reinsurance for the insurer may be bad for the reinsurer because they are conflicted about their interests.A good reinsurance strategy should consider the conflicts of interest between the insurer and the reinsurer.In this paper,we provide the optimal quota-share and stop-loss reinsurance from the perspective of both an insurer and a reinsurer.Then the optimality results of reinsurance are derived by minimizing linear combination of the VaRs of the cedent and the reinsurer under 16 reinsurance premium principles by using the Value-at-Risk(VaR)risk measure.For all cases we derive the optimal retention under these two reinsurance policies.