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Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation

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  • Boucher, Jean-Philippe
  • Denuit, Michel
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    Abstract

    The purpose of this paper is to explore and compare the credibility premiums in generalized zero-inflated count models for panel data. Predictive premiums based on quadratic loss and exponential loss are derived. It is shown that the credibility premiums of the zero-inflated model allow for more flexibility in the prediction. Indeed, the future premiums not only depend on the number of past claims, but also on the number of insured periods with at least one claim. The model also offers another way of analysing the hunger for bonus phenomenon. The accident distribution is obtained from the zero-inflated distribution used to model the claims distribution, which can in turn be used to evaluate the impact of various credibility premiums on the reported accident distribution. This way of analysing the claims data gives another point of view on the research conducted on the development of statistical models for predicting accidents. A numerical illustration supports this discussion.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4PK7P26-1/2/6282863970ded79e572214d39d7576f4
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 727-735

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:727-735

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    Web page: http://www.elsevier.com/locate/inca/505554

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    1. Morillo, Isabel & Bermudez, Lluis, 2003. "Bonus-malus system using an exponential loss function with an Inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 49-57, August.
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    Cited by:
    1. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    2. Miguel Santolino & Jean-Philippe Boucher, 2009. "Modelling the disability severity score in motor insurance claims: an application to the Spanish case," IREA Working Papers 200902, University of Barcelona, Research Institute of Applied Economics, revised Jan 2009.
    3. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    4. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," MPRA Paper 21587, University Library of Munich, Germany, revised 0020.
    5. Zhao, XiaoBing & Zhou, Xian, 2010. "Applying copula models to individual claim loss reserving methods," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 290-299, April.

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