Application of GLM and GAMLSS Models in Predictive Analysis of Motor Bodily Injury Claims

Automobile insurance is a type of insurance that offers financial coverage in the event of damage to the vehicle or physical injuries caused by road accidents. The analysis of claim amounts holds significant importance in the field of non-life insurance. Through the implementation of a model, insurers can more accurately forecast potential losses. The purpose of this study is to estimate the claim amounts using generalized linear models (GLM) and generalized additive models for location, scale, and shape (GAMLSS) and evaluate the effect of explanatory variables on claim amounts. This paper utilizes secondary data obtained from an Albanian insurance company from portfolio of Automobile Bodily Injury Claims, which consists of approximately 229 paid claims and includes eleven variables. The GAMLSS model proves to be the most suitable option due to its lowest AIC value and its ability to offer a wider range of distribution choices in comparison to the GLM model. The GAMLSS model with a lognormal distribution is identified as the optimal choice for insurance companies in this study, emphasizing that variables such as age, type and brand of the vehicle, type of claim and deferred period play a significant role in the estimation of claim amounts. The utilization of these models enables insurance companies to determine optimal insurance premiums for particular driver groups.