The claim process in an insurance risk model with uncertainty is traditionally described by an uncertain renewal reward process. However, the claim process actually includes two processes, which are called the report process and the payment process, respectively. An alternative way is to describe the claim process by an uncertain alternating renewal reward process. Therefore, this paper proposes an insurance risk model under uncertain measure in which the claim process is supposed to be an alternating renewal reward process and the premium process is regarded as a renewal reward process. Then, the paper also gives the inverse uncertainty distribution of the insurance risk process. The expression of ruin index and the uncertainty distribution of the ruin time are derived which both have explicit expressions based on given uncertainty distributions. Finally, several examples are provided to illustrate the modeling ideas.

中文翻译：

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不确定的交替续保保险风险模型

传统上，不确定性的续保奖励过程描述了具有不确定性的保险风险模型中的索赔过程。但是，索赔过程实际上包括两个过程，分别称为报告过程和支付过程。另一种方法是通过不确定的交替续订奖励过程来描述索赔过程。因此，本文提出了一种不确定措施下的保险风险模型，其中索赔过程被认为是交替的续签奖励过程，而保费过程被视为续签奖励过程。然后，本文还给出了保险风险过程的逆不确定性分布。根据给定的不确定度分布，推导了破坏指标的表达式和破坏时间的不确定性分布。