Modelling Motor Insurance Claims Frequency Using Poisson and Negative Binomial Models

Abstract

In non-life insurance, the distinctive challenge of estimating the count variable of interest at inception, coupled with the variability of claim costs generally gives insurance companies considerable concern about the chances and sizes of large claims, particularly for automobile insurance where it is required to manage large number of scenarios with a wide variety of risks. These count variables of losses represent individual risks, and need to be predicted, predominantly when the risk premium is to be computed for new policyholders, or when future premiums are adjusted based on past experience. Statistical modelling of count data therefore denotes a fundamental step in pricing of non-life insurance as it allows the classification of the risk factors and the estimation of the expected frequency of claims given the risk characteristics. This study presents the actuarial modelling of motor insurance claim occurrence using Nigerian motor insurance portfolio, to verify and estimate empirically an econometric model and the risk factors influencing the frequency of claims. The log-likelihood ratio and the information criteria was used in choosing the best model and the profile of policyholders with the highest degree of risk is determined. The modelling results are suggested for insurance companies in establishing fair and equitable risk pricing as this will help in appropriate premium determination, alleviate the effect of possible adverse selection and ensure premiums stability in the individual and aggregate portfolio.