Accounting for batch claim arrivals and fluctuation in premium income: from practice to theory

拟议研究计划的目标 破产理论模型旨在分析与保险业务相关的某些风险。更确切地说，它们包含有关各种保险特征的信息，如收取的保费、投资所得利息、索赔付款和其他费用，并提供评估相关风险的风险措施。一个重要的基本假设是，索赔一次一个。一般认为，如果情况不是这样，同时提出的索赔可以合并成一个单一的数额，然后解释为单一的索赔数额。另一个标准假设是，保费在一段时间内达到一个恒定的利率。 在过去的两年里，我一直与两名硕士生（Arezoo Tahmasebi女士和Yang Miao先生）和一名博士生一起工作。学生杨淼先生和两位同事布鲁斯琼斯教授和钟立教授对两组数据的分析。其中一个数据集集中在保费征收上。另一个数据集包含与多种汽车保险范围相关的索赔的详细信息。在Miao等人（2018）中，我们对数据进行了初步分析。我们发现，关于保险费和索赔的标准理论假设都是不准确的。 因此，本提案的目标是： 1.进一步分析保险费率数据，揭示保险费流向特征; 2.进一步分析索赔到达的数据，以揭示索赔流程的特征; 3.建立总保费的预测模型; 4.发展多个索赔到达的理论模型; 5.将上述模型合并到一个单一的破产模型中，以这种方式，将允许推导风险措施。 工作的新奇和预期意义 我们的目标是改进当前的框架，以弥补Miao et al.（2018）中发现的破产模型的缺陷。我们不知道以前有任何工作讨论这个问题。我们在Sendova和Minkova（2018）中的工作是第一次尝试以允许多个蛤蜊的方式调整当前的破产模型。然而，我们建议的计算程序并不足以灵活地处理所有类型的索赔保险数据。因此，需要进一步研究，以扩大选择范围。 研究与实践之间的差距是众所周知的。从业者很少使用破产模型。这项工作有可能说明如何保险数据可以用一个相当简单的方式来产生高度期望的风险措施。我们的长期目标是提出一个破产模型，反映保费和索赔流的实际特征。因此，我们将改进现有的模型，使它们更加现实，并说服从业者开始使用这些模型。

Objectives of the proposed research program Ruin theory models aim at analyzing certain risks related to the insurance business. More precisely, they incorporate information regarding various insurance characteristics such as premiums collected, interest earned on investments, claim payments, and other costs and provide risk measures that evaluate associated risks. One important underlying assumption is that claims arrive one at a time. It was generally believed that if that was not the case, simultaneously arriving claims could be aggregated into a single amount that would be then interpreted as a single claim amount. Another standard assumption is that premiums arrive at a constant rate over time. In the last two years, I have been working with two M.Sc. students (Ms. Arezoo Tahmasebi and Mr. Yang Miao) and one Ph.D. student (Mr. Yang Miao) as well as two colleagues (Prof. Bruce Jones and Prof. Zhong Li) on the analysis of two data sets. One of these data sets focusses on premium collection. The other data set contains detailed information on claims related to multiple car insurance coverages. In Miao et al. (2018), we performed preliminary analysis of the data. We have found that both standard theoretical assumptions concerning premiums and claims are inaccurate. As a result, the objectives of this proposal are: 1. to further analyze the data on premium rates to reveal characteristics of the premium flow; 2. to further analyze the data on claim arrivals to reveal characteristics of the claim flow; 3. to develop predictive models for the aggregate premiums; 4. to develop theoretical models for multiple claim arrivals; 5. to incorporate the above models into a single ruin model in such a way that will allow deducing risk measures. Novelty and expected significance of the work Our goal is to improve the current framework in a way that will remedy the deficiencies in ruin models that were found in Miao et al. (2018). We are not aware of any previous work discussing this issues. Our work in Sendova and Minkova (2018) was the first attempt to adapt the current ruin model in a way that will allow for multiple clams. Nevertheless, the counting process that we propose there is not sufficiently flexible for all types of claim insurance data. Thus, further studies are required to widen the range of options. The gap between research and practice is well known. Practitioners rarely use ruin models. This work has the potential to illustrate how insurance data can be used in a rather straightforward way to produce highly desired risk measures. Our long-term goal is to propose a ruin model that reflects the actual characteristics of the premium and the claim flows. We will thus improve upon the existing models in a way that will make them more realistic and will persuade practitioners to begin using such models.