Study Of Optimal Stop-loss Reinsurance

This thesis mainly studies the expected utility theory and the general princi-ples of expectations of premium in case of optimal re-insurance. The question of the optimum reinsurance is the important subjects of the precise mathematics of the non-life insurance, it relates the insurance company's capability to solve the problems of huge losses. In the face of the huge risk, it is necessary for the insur-ance company to disperse the risk and manage steadily through the reinsurance. So the research of the reinsurance is very important for insurance company. The most critical problem which lies in the optimal reinsurance study is that, under a certain optimization criterion, how the insurer determines the retention of the size and form of reinsurance.Expected utility maximization criterion is an important optimization crite-rion in the reinsurance, so we discuss this criterion and obtain a sufficient condi-tion for the existence of the best retention to the insurer under the general guide-lines for expected premium.At present the majority of the study under the expected utility of the optimal reinsurance only takes into account the interests of the insurer, while ignoring the interests of reinsurance. But the re-insurance is a kind of cooperative behavior, it should be taking into account the interests of both parties to achieve a win-win objective. For this purpose, in this thesis we take into account both the insurers and re-insurers'of interest,have some research under the conditions of restric-tions given by re-insurers and obtain the optimal solution of the two cases in the insurer's stop-loss reinsurance model. We also give a detailed analysis of the im-pact when limits the risk and concluded that, when the constraints are binding, the insurer must adjust their own insurance policy and increase the value of re-tention in order to meet the risk's restriction of re-insurers. In addition, we also demonstrate that the insurer's expected utility increases with the re-insurers' risk tolerance increased.