Application of the Generalized Linear Models in Actuarial Framework

TL;DR

This paper reviews the use of generalized linear models in actuarial science, focusing on model assessment, selection, and application to automobile claim prediction.

Contribution

It introduces model adequacy assessment methods and demonstrates their application in modeling automobile insurance claims.

Findings

Effective model assessment using deviance and scaled deviance

AIC as a comprehensive model selection criterion

Successful prediction of automobile claims using the chosen model

Abstract

This paper aims to review the methodology behind the generalized linear models which are used in analyzing the actuarial situations instead of the ordinary multiple linear regression. We introduce how to assess the adequacy of the model which includes comparing nested models using the deviance and the scaled deviance. The Akiake information criterion is proposed as a comprehensive tool for selecting the adequate model. We model a simple automobile portfolio using the generalized linear models, and use the best chosen model to predict the number of claims made by the policyholders in the portfolio.