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

拟议研究方案的目标 破产理论模型旨在分析与保险业务相关的某些风险。更准确地说，它们包含有关各种保险特征的信息，如收取的保费、投资赚取的利息、索赔付款和其他成本，并提供评估相关风险的风险衡量标准。一个重要的潜在假设是，索赔一次只有一项。人们普遍认为，如果情况并非如此，同时到达的索赔可合并为单一数额，然后将其解释为单一索赔额。另一个标准假设是保费随着时间的推移是恒定的。 在过去的两年里，我一直在与两名理科硕士合作。一名学生(Arezoo Tahmasebi女士和杨淼先生)和一名博士生(杨淼先生)以及两名同事(Bruce Jones教授和钟力教授)对两个数据集进行了分析。其中一个数据集中在高端收藏上。另一个数据集包含与多个汽车保险相关的索赔的详细信息。苗族等人。(2018)，我们对数据进行了初步分析。我们发现，关于保费和索赔的标准理论假设都是不准确的。 因此，这项建议的目标是： 1.进一步分析保费数据，揭示保费流动的特点； 2.进一步分析索赔到达的数据，揭示索赔流程的特点； 3.发展总保费的预测模型； 4.开发多个索赔到达的理论模型； 5.将上述模型合并为一个单一的破产模型，以便能够推定风险衡量标准。 作品的新颖性和预期意义 我们的目标是改进目前的框架，以弥补Miao等人在破产模型中发现的缺陷。(2018)。我们不知道以前有任何讨论这一问题的工作。我们在Sendova和Minkova(2018)的工作是第一次尝试以一种允许多个文蛤的方式来适应当前的破产模型。然而，对于所有类型的索赔保险数据，我们建议的计算过程并不足够灵活。因此，需要进一步研究以扩大选择范围。 研究和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以相当直接的方式使用保险数据来产生高度期望的风险度量。我们的长期目标是提出一个能反映保费和索赔流实际特征的破产模型。因此，我们将改进现有的模型，使其更加现实，并将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.