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Claim modeling and insurance premium pricing under a bonus-malus system in motor insurance

Ieosanurak Weenakorn, Khomkham Banphatree, Moumeesri Adisak

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 4

637--650

Accurately modeling claims data and determining appropriate insurance premiums are vital responsibilities for non-life insurance firms. This article presents novel models for claims that offer improved precision in fitting claim data, both in terms of claim frequency and severity. Specifically, we suggest the Poisson-GaL distribution for claim frequency and the exponential-GaL distribution for claim severity. The traditional method of assigning automobile premiums based on a bonus-malus system relies solely on the number of claims made. However, this may lead to unfair outcomes when an insured individual with a minor severity claim is charged the same premium as someone with a severe claim. The second aim of this article is to propose a new model for calculating bonus-malus premiums. Our proposed model takes into account both the number and size of claims, which follow the Poisson-GaL distribution and the exponential-GaL distribution, respectively. To calculate the premiums, we employ the Bayesian approach. Real-world data are used in practical examples to illustrate how the proposed model can be implemented. The results of our analysis indicate that the proposed premium model effectively resolves the issue of overcharging. Moreover, the proposed model produces premiums that are more tailored to policyholders’ claim histories, benefiting both the policyholders and the insurance companies. This advantage can contribute to the growth of the insurance industry and provide a competitive edge in the insurance market.

Optimal Parisian-Type Dividend Payments Penalized by the Number of Claims for the Classical and Perturbed Classical Risk Process

Czarna Irmina, Li Yanhong, Palmowski Zbigniew, Zhao Chunming

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

57--81

We consider the classical risk process (the case σ = 0) and the classical risk process perturbed by a Brownian motion (the case σ > 0). We analyze the expected NPV describing the mean of the cumulative discounted dividend payments paid up to the Parisian or classical ruin time and further penalized by the number of claims that appeared up to that time. We identify this function for a constant barrier strategy and we find sufficient conditions for this strategy to be optimal. We also analyze a numerical example of exponential claim sizes.