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A POSTERIORI RATEMAKING WITH PANEL DATA

Published online by Cambridge University Press:  23 April 2014

Jean-Philippe Boucher*
Affiliation:
Quantact/Département de mathématiques, UQAM, Montréal, Québec, Canada
Rofick Inoussa
Affiliation:
Quantact/Département de mathématiques, UQAM, Montréal, Québec, Canada E-Mail: inoussa.rofick_ayinde@uqam.ca

Abstract

Ratemaking is one of the most important tasks of non-life actuaries. Usually, the ratemaking process is done in two steps. In the first step, a priori ratemaking, an a priori premium is computed based on the characteristics of the insureds. In the second step, called the a posteriori ratemaking, the past claims experience of each insured is considered to the a priori premium and set the final net premium. In practice, for automobile insurance, this correction is usually done with bonus-malus systems, or variations on them, which offer many advantages. In recent years, insurers have accumulated longitudinal information on their policyholders, and actuaries can now use many years of informations for a single insured. For this kind of data, called panel or longitudinal data, we propose an alternative to the two-step ratemaking approach and argue this old approach should no longer be used. As opposed to a posteriori models of cross-section data, the models proposed in this paper generate premiums based on empirical results rather than inductive probability. We propose a new way to deal with bonus-malus systems when panel data are available. Using car insurance data, a numerical illustration using at-fault and non-at-fault claims of a Canadian insurance company is included to support this discussion. Even if we apply the model for car insurance, as long as another line of business uses past claim experience to set the premiums, we maintain that a similar approach to the model proposed should be used.

Type
Research Article
Copyright
Copyright © ASTIN Bulletin 2014 

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References

Bolancé, C., Denuit, M., Guillén, M. and Lambert, Ph. (2007) Greatest accuracy credibility with dynamic heterogeneity: The Harvey-Fernandes model. Belgian Actuarial Bulletin, 7 (1), 1418Google Scholar
Borgan, Ø., Hoem, J.M. and Norberg, R. (1981) A nonasymptotic criterion for the evaluation of automobile bonus systems. Scandinavian Actuarial Journal, 1981 (3), 265–178.Google Scholar
Boucher, J.-P., Denuit, M. and Guillén, M. (2007) Risk classification for claim counts: A comparative analysis of various zero-inflated mixed Poisson and hurdle models. North American Actuarial Journal, 11 (4), 110131.Google Scholar
Boucher, J.-P., Denuit, M. and Guillén, M. (2008) Models of insurance claim counts with time dependence based on generalisation of poisson and negative binomial distributions. Variance, 2 (1), 135162.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. Journal of Risk and Insurance, 76 (4), 821846.CrossRefGoogle Scholar
Boucher, J.-P. and Guillén, M. (2009) A survey on models for panel count data with applications to insurance. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, 103 (2), 277295.Google Scholar
Brown, R.L. (1988) Minimum bias with generalized LinearSSS models. PCAS, LXXV, 187217.Google Scholar
Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin, 4, 199207.CrossRefGoogle Scholar
Bühlmann, H. and Straub, E. (1970). GlaubwÄurdigkeit fÄur SchadensÄatze. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 70, 111133.Google Scholar
Denuit, M., Maréchal, X., Pitrebois, S. and Walhin, J.-F. (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. New York: Wiley.CrossRefGoogle Scholar
Frees, E. and Valdez, E.A. (2008) Hierarchical insurance claims modeling. Journal of the American Statistical Association, 103 (484), 14571469.Google Scholar
Gelman, A. and Robert, C.P. (2013) “Not only defended but also applied”: The perceived absurdity of Bayesian inference. The American Statistician, 67 (1), 15.CrossRefGoogle Scholar
Gelman, A. and Shalizi, C.R. (2013) Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology, 66, 838.CrossRefGoogle ScholarPubMed
Gerber, H.U. and Jones, D. (1975) Credibility formulas of the updating type. Transactions of the Society of Actuaries, 27, 3152.Google Scholar
Gilde, V. and Sundt, B. (1989) On bonus systems with credibility scales. Scandinavian Actuarial Journal, 1989 (1), 1322.Google Scholar
Gourieroux, C. and Jasiak, J. (2004) Heterogeneous INAR(1) model with application to car insurance. Insurance: Mathematics and Economics, 34, 177192.Google Scholar
Hachemeister, C. (1975) Credibility for regression models with applications to trend. In Credibility: Theory and Applications (ed. Kahn, P.M.) pp. 129163. New York: Academic Press.Google Scholar
Jewell, W. (1975) The use of collateral data in credibility theory: A hierarchical model. Giornale dell Istituto Italiano degli Attuari, 38, 116.Google Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Boston: Kluwer Academic Publisher.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd ed.London: Chapman and Hall.CrossRefGoogle Scholar
Norberg, R. (1976) A credibility theory for automobile bonus system. Scandinavian Actuarial Journal, 1976, 92107.CrossRefGoogle Scholar
Purcaru, O., Guillen, M. and Denuit, M. (2004) Linear credibility models based on time series for claim counts. Belgian Actuarial Bulletin, 4, 6274.Google Scholar
Ryder, J.M. (1976) Subjectivism - A reply in defense of classical actuarial methods (with discussion). Journal of the Institute of Actuaries, 103, 59112.CrossRefGoogle Scholar
Smyth, G. and Jorgensen, B. (2002) Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modelling. ASTIN Bulletin, 32 (1), 143157.Google Scholar
Sundt, B. (1988) Credibility estimators with deometric weights. Insurance: Mathematics and Economics, 7, 113122.Google Scholar
Young, V. and DeVylder, E.F. (2000) Credibility in favor of unlucky insureds. North American Actuarial Journal, 4 (1), 107113.Google Scholar