Modelling of Claim Counts in Automobile Third-party Liability Insurance

The aim of this paper is the analysis of the problem of modelling of claim counts in insurance that implies the study of variations of their occurrence through finding out the distribution which fits the observed data most adequately. As it is well known, in practice many cases of discontinuous variables can be modeled utilizing the Poisson distribution. However, examples of discontinuous random variables that do not adapt to this theoretical range model can often be found. One of these is the frequency of adverse events in motor third party liability insurance when some of the derived Poisson distributions may be more adequate, for example Poisson-Gamma (negative binomial) distribution, Poisson-Inverse Gaussian distribution, Poisson-LogNormal distribution, etc. Among the models that have been derived from the elements of Poisson processes, in this paper the model known as Good risk/bad risk (good driver/ ad driver) model is analyzed for the modeling of claim counts in automobile third-party liability insurance. In that sense, the most important aspects in the process of choosing the probability of claim numbers have been studied on a chosen sample from a Serbian insurance company and it has been found that appropriate sample analysis that was based upon the study of the previous experience of the insured was one of the key elements from the point of view of determining adequate premium systems.