A multilevel analysis of intercompany claim counts

In this paper, we use multilevel models to analyze data on claim counts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore. Our data comes from the financial records of automobile insurance policies followed over a period of nine years. The source contains a pooled experience of several insurers allowing us to analyze and model an "intercompany" experience data set, an area of research which is lacking in both the insurance and actuarial literatures. The multilevel nature of the data is due to: a vehicle is observed over a period of years and is insured by an insurance company under a 'fleet' policy. Fleet policies are umbrella-type policies issued to customers whose insurance covers more than a single vehicle with a taxicab company being a typical example. We investigate vehicle, fleet and company effects using various count distribution models (Poisson, negative binomial, zero-inflated and hurdle Poisson). The performance of these various models is compared; we demonstrate how our model can be used to update a priori premiums to a posteriori premiums, a common practice of experience-rated premium calculations.