Optimal Self-Retention Proportion For A Quota-Share Reinsurance Under VaR And CTE Risk Measures

Reinsurance is an insurance policy which transfers all or part of insurance business in order to scatter the risk to anther insurer.When insurance company faces to the catastrophoc risk, it is important to transfer the risk to reinsurance company.In reinsurance business,the most critical problem is how to choose optimal reinsurance,on the other hand,the study can provide strategies for insurance companies.Reinsurance companies required the risk which they could bear is not too large.So how to choose a rate to balance the risks of insurance and reinsurance becomes the key problem in this field.In this paper,we introduce reinsurance,including kinds of reinsurance strategies and premium calculation principles.Then we review some risk measures such as Mean-Variance measure, VaR risk measure and CTE risk measure,as well as the improved methods of ES risk measure. We show their optimization criterion and analyze their origins and characteristics separaterly. And we especially introduce VaR risk measure and CTE risk measure.VaR risk measure,which is widely used in the fields of bank,insurance,investment,and other financial institutions,is a risk measurement and a management tool.In order to make up the inner insignificance of VaR risk measure,CTE risk measure,which was first proposed by Rockafellar and Uryasev in the year of 2000(published online in 1999),is a substitute in the academia,it has been gradually improved later.Chapter3 shows relevant theorems about stop-loss reinsurance's optimal retention which under VaR and CTE risk measures as well as the corresponding optimal criterion,when premium principle adopts expected value principle.Based on results of Chapter3,we give and prove the sufficient condition for the existence of optimal self-retention proportion under VaR and CTE risk measures in Chapter4.Furthermore, we give the examples to verify the feasibility of the theorem.In the end,we show that it is reasonable the optimal retention proportion under CTE risk measure is smaller than that under VaR risk measure when the risk measureαis identical by several examples.