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

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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.