Generalized Linear Mixed Models for Dependent Compound Risk Models

23 Pages Posted: 2 Oct 2017

See all articles by Himchan Jeong

Himchan Jeong

Simon Fraser University - Department of Statistics and Actuarial Science

Emiliano A. Valdez

University of Connecticut - Department of Mathematics

Jae Youn Ahn

Ewha Womans University - Department of Statistics

Sojung Park

Seoul National University

Date Written: September 29, 2017

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 is sporadic interest in the actuarial literature exploring models that departs from this independence. In this article, we extend the work of Garrido et al. (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, we quantify and explain the contribution of the variability of claims among policyholders through the use of random effects using generalized linear mixed models (GLMMs). We calibrated our model using a portfolio of auto insurance contracts from a Singapore insurer where we observed claim counts and amounts from policyholders for a period of six years. We compared our results with the dependent GLM considered by Garrido et al. (2016), Tweedie models, and the case of independence. The dependent GLMM shows statistical evidence of positive dependence between frequency and severity. Using validation procedures, we find that the results demonstrate a more superior model when random effects are considered within a GLMM framework.

Keywords: Dependent frequency-severity models, random effects models, GLM, GLMM, ratemaking

JEL Classification: C10

Suggested Citation

Jeong, Himchan and Valdez, Emiliano A. and Ahn, Jae Youn and Park, Sojung, Generalized Linear Mixed Models for Dependent Compound Risk Models (September 29, 2017). Available at SSRN: https://ssrn.com/abstract=3045360 or http://dx.doi.org/10.2139/ssrn.3045360

Himchan Jeong

Simon Fraser University - Department of Statistics and Actuarial Science ( email )

8888 University Drive
Burnaby, British Columbia V5A1S6
Canada

Emiliano A. Valdez (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U-1009
Storrs, CT 06269-1009
United States

HOME PAGE: http://www.math.uconn.edu/~valdez

Jae Youn Ahn

Ewha Womans University - Department of Statistics ( email )

Seoul 120-
Korea, Republic of (South Korea)

Sojung Park

Seoul National University ( email )

Kwanak-gu
Seoul, 151-742
Korea, Republic of (South Korea)

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