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TESTING FOR RANDOM EFFECTS IN COMPOUND RISK MODELS VIA BREGMAN DIVERGENCE

Published online by Cambridge University Press:  02 July 2020

Himchan Jeong Open the ORCID record for Himchan Jeong [Opens in a new window]
Himchan Jeong*
Affiliation:
Department of Statistics & Actuarial Science Simon Fraser University Burnaby, BCV5A 1S6, Canada E-Mail: himchan_jeong@sfu.ca
*
E-Mail: himchan_jeong@sfu.ca
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Abstract

The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practices, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim datasets, there have been some trials of incorporating unobserved heterogeneity of each policyholder from the repeated observations. To achieve this goal, random effects models have been proposed, but theoretical discussions of the methods to test the presence of random effects in GLM framework are still scarce. 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) Journal of Multivariate Analysis, 124, 371–383]. We can apply model diagnostics derived from the Bregman divergence for testing robustness of a chosen prior by the modeler to possible misspecification of prior distribution both on the naive model, which assumes that random effects follow a point mass distribution as its prior distribution, and the proposed model, which assumes a continuous prior density of random effects. This approach provides insurance companies a concrete framework for testing the presence of nonconstant 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.

Keywords

Two-part frequency-severity modelcompound random effects modelBregman divergenceBayesian sensitivity analysismodel selectionprior elicitationgeneralized linear model (GLM)generalized Pareto (GP)C11C23C52
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 777 - 798
Copyright
© 2020 by Astin Bulletin. All rights reserved

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