A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance

Fevi Novkaniza; Irene Devina Putri; Rahmat Al Kafi; Sindy Devila

doi:10.31764/jtam.v9i1.27837

A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance

Fevi Novkaniza, Irene Devina Putri, Rahmat Al Kafi, Sindy Devila

Abstract

This study develops and applies the Poisson-Gamma Hierarchical Generalized Linear Model (PGHGLM) to address the challenge of determining accurate and fair premium rates in vehicle insurance. The PGHGLM models a mixture distribution for the response variable, influenced by random effects, and employs a logarithmic link function. Parameter estimation is conducted using the maximum likelihood method. However, since analytical estimation is not feasible, the numerical conjugate gradient method, specifically the Fletcher-Reeves algorithm, is utilized. The implementation of the PGHGLM uses the longitudinal Claimslong dataset, incorporating driver age as a covariate. The main contribution of this research lies in integrating a priori risk classification with a posteriori adjustment based on longitudinal claim frequency data. For datasets without covariates, trend parameters are incorporated into the model. For datasets with covariates, such as driver age, the average claim frequency is computed for each age category. Results show that posteriori premium rates increase with rising claim frequency from the previous year, with higher claim frequencies leading to larger rate adjustments in the subsequent year. Through the PGHGLM, a posteriori premium rate estimates are obtained for each age group of vehicle insurance policyholders. This study demonstrates the practical application of the PGHGLM in calculating precise premium rates. By analyzing a longitudinal vehicle insurance dataset, the model generates annual a posteriori premium rates tailored to age groups. These findings underscore the PGHGLM’s robust methodological framework and its potential to enhance premium fairness, enable risk-adjusted pricing, and better tailor insurance products to diverse policyholder profiles.

Keywords

Claim Frequency; Conjugate Gradient; Longitudinal Data; Maximum Likelihood; Random effects.

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DOI: https://doi.org/10.31764/jtam.v9i1.27837