Uncertain insurance risk process with single premium and multiple classes of claims
Uncertain insurance risk process with single premium and multiple classes of claims
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单一保费和多种索赔类别的不确定保险风险流程
DOI：
10.1007/s12652-020-02486-x
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发表时间：
2020-08-29
影响因子：
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通讯作者：
Yang, Xiangfeng
中科院分区：
文献类型：
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作者：
Liu, Zhe;Yang, Xiangfeng
传统的保险风险过程是在概率论的框架下考虑的，其前提是估计的分布函数与实际频率足够接近。然而，由于经济或技术原因，有时数据不可用或难以获得，例如当我们考虑一种新的保险产品或贵重武器的保险时。在这种情况下，报销政策是基于专家的相信程度，其范围比实际频率大得多。因此，我们应该采用不确定性保险风险模型来更好地处理经营保险公司的人为不确定性。注意到保险公司支付不同类型的风险以及客户到达和付款的不确定性，我们研究了具有多个索赔类别的不确定保险风险过程，其中保费过程遵循不确定的续订过程。然后导出了破产指数的表达式和破产时间的不确定性分布。通过一些数值示例和一个实际数据示例来获得更多的见解。
Traditionally an insurance risk process is considered under the framework of probability theory with a prerequisite that the estimated distribution function is close enough to the real frequency. However, due to economic or technological reasons, sometimes data are unavailable or difficult to obtain, such as when we consider a new insurance product or insurance for valuable weapons. Under these situations, reimbursement policies are based on experts’ belief degree, which has a much wider range than the real frequency. As a result, we should employ uncertain insurance risk models to better deal with human uncertainty in running an insurance company. Noticing the fact that an insurance company pays for different kinds of risks and the uncertainty of the customer’s arrivals and payments, we investigate an uncertain insurance risk process with multiple classes of claims where the premium process follows an uncertain renewal process. Then we derive expressions for the ruin index and the uncertainty distribution of the ruin time. Some numerical examples and a real data example are performed to capture more insights.