Optimal Retentions For A Stop-Loss Reinsurance With Dependent Risks Under The VaR And CTE Risk Measures

In recent years, although the study on dependent risk is increasing rapidly, very few of these deal with the problem in relation to reinsurance. In this paper, two optimization criteria are developed including Value-at–risk (VaR) and Conditional-tail-expectation (CTE) to consider the optimal stop-loss reinsurance retentions for two dependent risks from the insurance point. Firstly, the determination of optimal retention in a stop-loss reinsurance of one risk is proposed. Both optimization criteria yield the same simple retentions, but the optimal conditions for the CTE criterion are less restriction than the corresponding VaR criterion. Secondly, the expected value principle is used with the number of claims is generated by bivariate Poisson distribution, then the optimal solution and conditions which exist are obtained. Then the variance premium principle with the same model is studied .As a result, the retention and the conditions under VaR-based and CTE-based are showed which the CTE-based solution are more simple. At last, the result illustrated by some examples.