随机巨灾索赔相依风险模型的动态最优再保险

Dynamic optimal reinsurance for stochastic catastrophe with dependent claim risks

在索赔风险时变、相依条件下,建立随机巨灾的可调态再保险模型.在指明超额赔款再保险为最优分保形式的基础上,讨论并发现目标函数随自留巨灾风险水平的增大,在任意相依结构下均先减后增的变化定理,从而获得了自留向量的一般性显式表达式.根据巨灾风险的特征,还在一类特定的相依结构下,以自留风险的期望效用和方差为优化目标,对自留向量进行了更为明确的表示并给出具体示例.结果表明,随着巨灾风险相依强度的上升,分保的满意度降低,经营稳定性减弱,对保险公司的负面影响很大.此时,为实现客观风险下的分保目标最优,常规风险的自留水平应随之增大,体现了动态再保险的优越性.

An adjustable reinsurance model for stochastic catastrophe was established under the conditions that the claim risks are time-varying and dependent.On the basis of showing the optimality of excess-of-loss reinsurance treaty,discussions found that the objective functions under arbitrary dependence structure are decreasing first and then turn out to be increasing as the retention level of catastrophe risk increases,thus the explicit expression of the retention vector was given in a general form.According to the characteristic of catastrophe risks,the retention vector under a particular dependence structure was further presented as well and a concrete example was studied to optimize the expected utility or variance of the retained risks.The result shows that both the satisfaction of reinsurance and the stability of business reduce as the dependence intensity of catastrophe risks increase,the negative effect to the insurer is very obvious.Meanwhile,to optimize the objects of reinsurance with objective risks,the risk retention level in usual case shall also rise up,which reflects the superiority of dynamic reinsurance.