The Study Of Optimal Reinsurance Under Joint Survival Probability Criterion

Reinsurance is an insurance policy which transfers all or part of insurance business in order to scatter the risk to another insurer. In this paper , we consider both the insurer's benefits and reinsurer's benefits by using their joint survival probability as the criteria for determining the optimal reinsurance.Let X be the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes parts of its loss, say f ( X ),where f ( x ) is increasing convex and known as a ceded loss function . In this paper , we prove that the function with the form of , ,the optimal ceded loss function under joint survival probability criterion. To practice common reinsurance form , we derive optimal quota- share reinsurance strategy , optimal stop-loss reinsurance strategy and optimal change-loss reinsurance strategy under the expectation premium principle. A number of concrete numerical examples are also shown.In practice , an insurance company can simultaneously transfer the initial loss to two or more reinsurance companies . Therefore , this paper formulate and study optimal reinsurance model with m reinsurance companies under the joint survival probability ctiteria . The results indicate that the joint survival probability increases if more reinsurance companies take risk. In other words, in order to improve survival probability and guarantee the stability of the business , the original insurance company should cedes parts of its loss to more reinsurance companies.