Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-30T04:35:05.266Z Has data issue: false hasContentIssue false
  • English
  • Français

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: jfrees@bus.wisc.edu
Emiliano A. Valdez
Affiliation:
University of Connecticut, USA, E-mail: valdez@math.uconn.edu
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Angers, J.-F., Derjardins, D., Dionne, G. and Guertin, F. (2006) Vehicle and fleet random effects in a model of insurance rating for fleets of vehicles. ASTIN Bulletin, 36(1), 25–77.Google Scholar
Antonio, K. and Beirlant, J. (2007) Actuarial statistics with generalized linear mixed models. Insurance: Mathematics and Economics, 40(1), 58–76.Google Scholar
Bolancé, C., Guillén, M. and Pinquet, J. (2003) Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on random effects. Insurance: Mathematics and Economics, 33, 273–282.Google Scholar
Boucher, J.-P., Denuit, M. and Guillén, M. (2007) Risk classification for claim counts: mixed Poisson, zero-inflated mixed Poisson and hurdle models. North American Actuarial Journal, 11(4), 110–131.Google Scholar
Boucher, J.-P., Denuit, M. and Guillén, M. (2008) Modeling of insurance claim counts with hurdle distribution for panel data. Advances in Mathematical and Statistical Modeling: Statistics for Industry and Technology, Birkhauser Boston, Inc.Google Scholar
Boucher, J.-P., Denuit, M. and Guillén, M. (2009) Number of accidents or number of claims? An approach with zero-inflated Poisson models for panel data. The Journal of Risk and Insurance, forthcoming.CrossRefGoogle Scholar
Cameron, A.C. and Trivedi, P.K. (1998) Regressionanalysis of count data. Cambridge University Press.Google Scholar
Deb, P., Munkin, M.K. and Trivedi, P.K. (2006) Private insurance, selection and health care use: a Bayesian analysis of a Roy-type model. Journal of Business & Economic Statistics, 24(4), 403–415.Google Scholar
Denuit, M., Marechal, X., Pitrebois, S. and Walhin, J.-F. (2007) Actuarial Modelling Of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. Wiley.Google Scholar
Desjardins, D., Dionne, G. and Pinquet, J. (2001) Experience rating scheme for fleets of vehicles. ASTIN Bulletin, 31(1), 81–105.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1989) A generalization of actuarial automobile insurance rating models: the Negative Binomial distribution with a regression component. ASTIN Bulletin, 19, 199–212.CrossRefGoogle Scholar
Frees, E.W. and Valdez, E.A. (2008) Hierarchical insurance claims modeling. Journal of the American Statistical Association, 103(484), 1457–1469.Google Scholar
Frees, E.W., Young, V.R. and Luo, Y. (1999) A longitudinal data analysis interpretation of credibility models. Insurance: Mathematics and Economics, 24(3), 229–247.Google Scholar
Gelman, A. and Hill, J. (2007) Applied Regressionand Multilevel (Hierarchical) Models. Cambridge University Press, Cambridge.Google Scholar
Goldstein, H. (2003) Multilevel Statistical Models. Oxford University Press.Google Scholar
Hickman, J.C. and Heacox, L. (1999) Credibility theory: the cornerstone of actuarial science. North American Actuarial Journal, 3(2), 1–8.Google Scholar
Iverson, B., Luff, J., Siegel, S. and Stryker, R. (2007) The SOA: A place for research – answer to all yourquestions about the research done by the SOA. The Actuary Magazine, October/November.Google Scholar
Jewell, W.S. (1975) The use of collateral data in credibility theory: a hierarchical model. Giornale dell'Instituto Italiano degli Attuari, 38, 1–6.Google Scholar
Kaas, R., Goovaerts, M., Dhaene, J. and Denuit, M. (2008) Modern actuarial risk theory using R. Springer-Verlag, Berlin.Google Scholar
Kreft, I.G.G. and deLeeuw, J. (1998) Introducing Multilevel Modeling. Sage Publications, London.CrossRefGoogle Scholar
Lee, A., Wang, K., Scott, J., Yau, K. and Mclachlan, G. (2006) Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros. Statistical Methods In Medical Research, 15(1), 47–61.Google Scholar
Lemaire, J. (1995) Bonus-malus systems in automobile insurance. Springer-Verlag, New York.Google Scholar
Norberg, R. (1986) Hierarchical credibility: analysis of a random effect linear model with nested classification. Scandinavian Actuarial Journal, pages 204–222.Google Scholar
Pinquet, J. (1997) Allowance for cost of claims in bonus-malus systems. ASTIN Bulletin, 27(1), 33–57.CrossRefGoogle Scholar
Pinquet, J. (1998) Designing optimal bonus-malus systems from different types of claims. ASTIN Bulletin, 28(2), 205–229.CrossRefGoogle Scholar
Pinquet, J., Guillén, M. and Bolancé, C. (2001) Allowance for age of claims in bonus-malus systems. ASTIN Bulletin, 31(2), 337–348.Google Scholar
Raudenbush, S.W. and Bryk, A.S. (2002) Hierarchical Linear Models: Applications and Data Analysis Methods. Sage Publications, Thousand Oaks.Google Scholar
Snijders, T.A.B. and Bosker, R.J. (1999) Multilevel Analysis: an introduction to basic and advanced multilevel modeling. Sage Publications, London.Google Scholar
Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and Van Der Linde, A. (2002) Bayesian measures of model complexity and it. Journal of the Royal Statistical Society, Series B, 64(3), 583–639.Google Scholar
Sundt, B. (1980) A multi-level hierarchical credibility regression model. Scandinavian Actuarial Journal, 25–32.Google Scholar
Taylor, G. (1979) Credibility analysis of a general hierarchical model. Scandinavian Actuarial Journal, pages 1–12.Google Scholar
Winkelmann, R. (2003) Econometric Analysis of Count Data. Springer-Verlag, Berlin.Google Scholar
Yau, K., Wang, K. and Lee, A. (2003) Zero-inflated negative binomial mixed regression model. Biometrical Journal, 45(4), 437–452.Google Scholar
Yip, K. and Yau, K. (2005) On modeling claim frequency data in general insurance with extra zeros. Insurance: Mathematics and Economics, 36, 153–163.Google Scholar