Generalized Linear Mixed Models for Dependent Compound Risk Models

Abstract

In ratemaking, calculation of a pure premium has traditionally been based on modeling frequency and severity in an aggregated claims model. For simplicity, it has been a standard practice to assume the independence of loss frequency and loss severity. In recent years, there has been sporadic interest in the actuarial literature exploring models that depart from this independence. In this paper, the authors extend the work of Garrido, Genest, and Schulz (2016), which uses generalized linear models (GLMs) that account for dependence between frequency and severity and simultaneously incorporate rating factors to capture policyholder heterogeneity. In addition, they quantify and explain the contribution of the variability of claims among policyholders through the use of random effects using generalized linear mixed models (GLMMs). The authors calibrated their model using a portfolio of auto insurance contracts from a Singapore insurer where they observed claim counts and amounts from policyholders for a period of six years. They compared their results with the dependent GLM considered by Garrido, Genest, and Schulz; Tweedie models; and the case of independence. The dependent GLMM shows statistical evidence of positive dependence between frequency and severity. Using validation procedures, the authors find that the results demonstrate a superior model when random effects are considered within a GLMM framework.

Volume
14
Issue
1
Year
2021
Keywords
Random effects models, GLM, GLMM, Ratemaking, Dependent frequency-severity models, predictive analytics
Publications
Variance
Authors
Emiliano A Valdez
Himchan Jeong
Jae Youn Ahn
Sojung Carol Park
Formerly on syllabus
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