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

Listed author(s):
  • Boucher, Jean-Philippe
  • Denuit, Michel
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    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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    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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    1. Boucher, Jean-Philippe & Denuit, Michel, 2006. "Fixed versus Random Effects in Poisson Regression Models for Claim Counts: A Case Study with Motor Insurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(01), pages 285-301, May.
    2. Young, Virginia R., 1996. "Credibility and Persistency," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(01), pages 53-69, May.
    3. Walhin, Jean François & Paris, José, 2000. "The True Claim Amount and Frequency Distributions within a Bonus-Malus System," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(02), pages 391-403, November.
    4. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    5. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    6. 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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