A Multilevel Analysis of Intercompany Claim Counts

It is common for professional associations and regulators to combine the claims of several insurers into a database known as an "intercompany" experience data set. In this paper, we analyze data on claims accounts 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. Because the source includes a pooled experience of several insurers, we are able to study company effects on claim behavior, an area that has not been systematically addressed in either the insurance or the actuarial literatures.

We analyze this intercompany experience using multilevel models. The multi-level 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. We investigate vehicle, fleet and company effects using various count distribution models (Poisson, negative binomal, 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. Through this formal model structure, we provide insights into effects that company-specific practice has on claims experience, even after controlling for vehicle and fleet effects.

Keywords: Actuarial science, hierarchal model; multi-level model; experience rating; bonus-malus factors; generalized count distributions.