A multilevel analysis of intercompany claim counts

For the construction of a fair tariff structure in automobile insurance, insurers classify the risks that they underwrite. The idea behind this risk classification is to subdivide the portfolio into classes of risks with similar profiles. While some insurers may have sufficient historical data, several others may not have significant volume of experience data in order to produce reliable claims predictions to help enhance their risk classification systems. A database containing a pooled experience of several insurers thereby helps to produce a more fair, reliable, and equitable premium structure for all risks concerned. Research and analysis of such "intercompany" insurance experience data is lacking in both the actuarial and statistical literature. Its benefits goes beyond the insurer; reinsurers (i.e. insurers of insurers) together with regulators also benefit from statistical models of this type of data because they typically deal with analyzing the experience of a collection of insurers.
In this paper, we use multilevel models to analyze the 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 multilevel nature of the data is due to the following: a certain vehicle is observed over a period of years and is insured by a particular insurance company under a certain ‘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 show how intercompany data lead to a priori premiums and a posteriori corrections to these initial premiums. Specific focus is made in understanding the intercompany effects using various count distribution models (Poisson, negative binomial, zero-inflated and hurdle Poisson). The performance of these various models is compared; we also investigated how to use the historical claims of a
company, fleet and/or vehicle in order to correct for the premium initially set.