Predictive analysis in insurance: An application of generalized linear mixed models

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 Bühlmann 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.