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HimChan Jeong's Abstract

The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practice, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim dataset, there have been some trials of incorporating unobserved heterogeneity of each policyholder
from the repeated measurements. To achieve this goal, random effects model has been proposed but there was less theoretical discussion on the methods to test the presence of random effects in GLM framework.

In this article, the concept of Bregman divergence is explored, which has some good properties for statistical modeling and can be connected to diverse model selection diagnostics as in Goh and Dey (2014). We can apply model diagnostics derived from the Bregman divergence for testing robustness of priors both on the naive model, which assumes that random effect has point mass as its prior density, and the proposed model, which assumes a continuous prior density of random effect. This approach provides the insurance companies a concrete framework for testing the presence of random effects in both claim frequency and severity and
furthermore appropriate hierarchical model which can explain both observed and unobserved heterogeneity of the policyholders for insurance ratemaking. Both models are calibrated using a claim dataset from the Wisconsin Local Government Property Insurance Fund which includes both observed claim counts and
amounts from a portfolio of policyholders.