Skip to main content
×
Home
    • Aa
    • Aa

A POSTERIORI RATEMAKING WITH PANEL DATA

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

Copyright
Corresponding author
E-Mail: boucher.jean-philippe@uqam.ca
Linked references
Hide All

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.

E. Frees and E.A. Valdez (2008) Hierarchical insurance claims modeling. Journal of the American Statistical Association, 103 (484), 14571469.

A. Gelman and C.P. Robert (2013) “Not only defended but also applied”: The perceived absurdity of Bayesian inference. The American Statistician, 67 (1), 15.

A. Gelman and C.R. Shalizi (2013) Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology, 66, 838.

V. Gilde and B. Sundt (1989) On bonus systems with credibility scales. Scandinavian Actuarial Journal, 1989 (1), 1322.

J. Lemaire (1995) Bonus-Malus Systems in Automobile Insurance. Boston: Kluwer Academic Publisher.

P. McCullagh and J.A. Nelder (1989) Generalized Linear Models, 2nd ed.London: Chapman and Hall.

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 46 *
Loading metrics...

Abstract views

Total abstract views: 237 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th June 2017. This data will be updated every 24 hours.