Experience Rating in Motor Insurance Industry Using Glm

Abstract

Motor insurance is a necessity in most States and thus records an overwhelming number of claims in any given period. Actuaries therefore need to determine a reward structure in a manner that is fair to the policyholder and with certainty of maximum pro ts to the insurer. This paper aims at reviewing the methodology behind the generalized linear models used in the pricing of premiums paid in by policyholders in the motor insurance industry based on the general risk factors; risk, policyholder and vehicle characteristics, policy type among others that an insurer may wish to include in their rating plan. Negative binomial regression is presented with comparison to the Poisson regression as rating techniques among others such as credibility, BM, multi-state and BS approaches. Even with all the explanatory variables that an insurer could consider, motor insurance industry will experiences heterogeneity such as temperament and drinking behaviour of drivers. An accurate rating system is crucial to the actuary as it would precisely re ect the losses. Categorizing such losses based on the risk factors is very essential in determining the accuracy of a given rating method, in the fact that, risk factors would determine which level of a particular risk factor causes more claims which would result to the biggest loss and therefore should pay the highest premium, and as well as ones that causes little claims which would result to the smallest loss, to be charged the lowest premium. Based on a sample of a simple portfolio of secondary motor insurance claims data from a Motor Insurance Brokerage rm in Kenya, main predictor variables that would be advisable for insurers to include in their rating purposes are then determined with all the statistical computations done using R. This paper considers GLM as an appropriate rating system that would incorporate both the observable and the unobservable factors expected in a rating plan.