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  • Jean-Philippe Boucher (a1) and Rofick Inoussa (a2)

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J.-P. Boucher , M. Denuit and M. Guillén (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.

J.-P. Boucher , M. Denuit and M. Guillén (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.

M. Denuit , X. Maréchal , S. Pitrebois and J.-F. Walhin (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. New York: Wiley.

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R. Norberg (1976) A credibility theory for automobile bonus system. Scandinavian Actuarial Journal, 1976, 92107.

V. Young and E.F. DeVylder (2000) Credibility in favor of unlucky insureds. North American Actuarial Journal, 4 (1), 107113.

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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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