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Modelling Motor Insurance Claim Severity Using Generalized Linear Models

Abstract

The study examines the modelling of motor insurance claim severity using generalized linear models, with emphasis on the application of statistical methods for estimating the financial magnitude of motor insurance claims. Claim severity is an important component of insurance loss experience because the amount paid for individual claims can vary considerably across policyholders and incidents. Accurate modelling of claim severity is therefore essential for effective risk assessment, premium determination, claims reserving, underwriting, and overall actuarial decision-making. The study will investigate the suitability of generalized linear models (GLMs) for modelling variations in motor insurance claim severity. It will examine the extent to which relevant characteristics of policyholders, vehicles, and insurance policies can explain differences in claim amounts. The study will also consider the ability of GLMs to accommodate the skewed and non-normal characteristics commonly associated with insurance claim severity data. The study will further analyse appropriate probability distributions and link functions for modelling motor insurance claim severity within the generalized linear modelling framework. Variables such as driver age, vehicle type, driving experience, claims history, policy characteristics, and other relevant risk factors will be considered where suitable data are available. Attention will be given to model specification, parameter estimation, goodness-of-fit, and the predictive performance of the selected models. A quantitative research approach will be adopted using relevant historical motor insurance claims and policy data. Descriptive statistical techniques will be employed to examine the distribution and characteristics of claim amounts. Appropriate generalized linear models will then be fitted to the data using suitable probability distributions, such as the Gamma and Inverse Gaussian distributions, and appropriate link functions. Model performance will be assessed using statistical and actuarial measures of goodness-of-fit and predictive accuracy. The study is expected to reveal that generalized linear models can provide useful estimates of motor insurance claim severity and identify factors associated with differences in claim amounts. Models that appropriately account for the skewness and variability of claim severity are expected to produce more reliable estimates than methods based on restrictive assumptions of normally distributed claim amounts. The findings may also reveal differences in the performance of alternative GLM specifications. The study is further expected to establish that effective modelling of claim severity can improve motor insurance pricing, underwriting, claims reserving, and risk management. Accurate estimates of expected claim amounts may help insurers develop premiums that better reflect anticipated losses and improve their ability to manage financial exposure. The findings may also provide useful guidance to actuarial practitioners in applying generalized linear models to motor insurance claims data. The study concludes that generalized linear models provide a suitable framework for analysing and predicting motor insurance claim severity. It is therefore recommended that insurance companies should apply appropriate GLM techniques when modelling claim amounts, carefully evaluate distributional assumptions and model performance, and regularly update their models with new claims experience to maintain reliable actuarial estimates and effective motor insurance risk management.

Keywords: Motor Insurance, Claim Severity, Generalized Linear Models, GLM, Insurance Claims, Claims Modelling, Actuarial Modelling, Loss Severity, Statistical Modelling, Gamma Distribution, Inverse Gaussian Distribution, Risk Assessment, Insurance Pricing, Claims Reserving, Predictive Modelling.