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Experience Rating and Credibility

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  • Bühlmann, Hans

Abstract

Classical statistics deals with the following standard problem of estimation:Given: random variables X1, X2 … Xn independent, identically distributed, andobservations x1, X2 … xn,Estimate: parameter (or function thereof) of the distribution function common to all Xi.It is not surprising that the “classical actuary†has mostly been involved in solving the actuarial equivalent of this problem in insurance, namelyGiven: risks R1R2 … Rn no contagion, homogeneous group,Find: the proper (common) rate for all risks in the given class.There have, of course, always been actuaries who have questioned the assumptions of independence (no contagion) and/or identical distribution (homogeneity). As long as ratemaking is considered equivalent to the determination of the mean, there seem to be no additional difficulties if the hypothesis of independence is dropped. But is there a way to drop the condition of homogeneity (identical distribution)?

Suggested Citation

  • Bühlmann, Hans, 1967. "Experience Rating and Credibility," ASTIN Bulletin, Cambridge University Press, vol. 4(3), pages 199-207, July.
    • Handle: RePEc:cup:astinb:v:4:y:1967:i:03:p:199-207_00
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    Cited by:

    1. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 205-220, November.
    2. J. Pinquet & M. Guillén & C. Bolancé, 2000. "Long-range contagion in automobile insurance data : estimation and implications for experience rating," THEMA Working Papers 2000-43, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Garnadi, Agah D. & Nurdiati, Sri & Erliana, Windiani, 2017. "Univariate Credibility as a Boundary-Value Problem, A Symbolic Green’s Function Method (Regular Case)," INA-Rxiv wg7qa, Center for Open Science.
    4. Linacre, Nicholas A. & Burgman, Mark A. & Ades, Peter K. & Stewart-Oaten, Allen, 2005. "Incorporating collateral information using an adaptive management framework for the regulation of transgenic crops:," EPTD discussion papers 137, International Food Policy Research Institute (IFPRI).
    5. Quigley, John & Bedford, Tim & Walls, Lesley, 2007. "Estimating rate of occurrence of rare events with empirical bayes: A railway application," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 619-627.

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