• Communications for Statistical Applications and Methods
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• v.30 no.5
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• pp.437-451
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• 2023

Generalized linear models and generalized linear mixed models (GLMMs) are fundamental tools for predictive analyses. In insurance, GLMMs are particularly important, because they provide not only a tool for prediction but also a theoretical justification for setting premiums. Although thousands of resources are available for introducing GLMMs as a classical and fundamental tool in statistical analysis, few resources seem to be available for the insurance industry. This study targets insurance professionals already familiar with basic actuarial mathematics and explains GLMMs and their linkage with classical actuarial pricing tools, such as the Buhlmann premium method. Focus of the study is mainly on the modeling aspect of GLMMs and their application to pricing, while avoiding technical issues related to statistical estimation, which can be automatically handled by most statistical software.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1181-1190
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• 2010

When an insurer develops an insurance product, it is very critical to determine reasonable premiums, which is directly related to insurer's profits. There are three methods to determine premiums. Frist, the insurer utilizes premiums paid to the similar cases to the current one. Second, the insurer calculates premiums based on policyholder's past records. The last method is to combine the first with the second one. Based on the three methods, there are two major theories determining premiums, Limited Fluctuation Credibility Theory not based on statistical models and Greatest Accuracy Credibility Theory based on statistical models. There are well-known methods derived from Greatest Accuracy Credibility Theory, such as, Buhlmann model and Buhlmann-Straub model. In this paper, we extend the Buhlmann-Straub model to accommodate the fact that variability grows according to the number of data in practice and suggest a new non-parametric method to estimate the premiums. The suggested estimation method is also applied to the data gained from simulation and compared with the existing estimation method.