最优比例与超额损失组合再保险下的破产概率

本文站在保险人的立场上,讨论了保险公司的最优组合再保险问题.通过纯粹比例再保险,纯粹超额损失再保险,或者这两类再保险的组合方式,把保险公司的部分风险分担出去.在最大化调节系数的最优准则下,我们得出了布朗运动模型和复合Poisson模型中最优值的显示表达,并且给出了复合Poisson模型中最优策略下破产概率的最小指数上界.我们还得出结论:在一定的条件下,总存在一种纯粹超额损失再保险策略比任何一类组合再保险策略都要好.最后,通过一些数例和图表来进一步说明我们在文中所获得的结论.

Ruin Probabilities under Optimal Combining Quota-Share and Excess of Loss Reinsurance

In this paper, we study the optimal retentions for an insurance company, which intends to reinsure its risk by means of a pure proportional treaty, a pure excess of loss treaty or any combination of the two. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are given not only for the Brownian motion risk model but also for the compound Poisson risk model. Moreover, a smallest exponential upper bound for the ruin probability is obtained. We also conclude that, under some conditions, there exists a pure excess of loss reinsurance strategy which is better than any combinational reinsurance strategy. Some numerical examples are presented, which illustrate the results of this paper.