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A Multilevel Analysis of Intercompany Claim Counts

Published online by Cambridge University Press:  09 August 2013

Katrien Antonio ,
Edward W. Frees  and
Emiliano A. Valdez
Edward W. Frees
Affiliation:
University of Wisconsin in Madison, USA, E-mail: [email protected]
Emiliano A. Valdez
Affiliation:
University of Connecticut, USA, E-mail: [email protected]
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Abstract

It is common for professional associations and regulators to combine the claims experience of several insurers into a database known as an “intercompany” experience data set. In this paper, we 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. Because the source contains 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 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. 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. 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 sciencehierarchical modelmultilevel modelexperience ratingbonus-malus factorsgeneralized count distributions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 151 - 177
Copyright
Copyright © International Actuarial Association 2010

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