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Credibility in Favor of Unlucky Insureds

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  • Virginia Young
  • F. De Vylder

Abstract

The classical Bühlmann credibility formula estimates the hypothetical mean of a particular insured, or risk, by a weighted average of the grand mean of the collection of risks with the sample mean of the given insured. If the insured is unfortunate enough to have had large claims in the previous policy period(s), then the estimate of future claims for that risk will also be large. In this paper we provide actuaries with a method for not overly penalizing an unlucky insured while still targeting the goal of accuracy in the estimate. We propose a credibility estimator that minimizes the expectation of a linear combination of a squared-error term and a first-derivative term. The squared-error term measures the accuracy of the estimator, while the first-derivative term constrains the estimator to be close to constant.

Suggested Citation

  • Virginia Young & F. De Vylder, 2000. "Credibility in Favor of Unlucky Insureds," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(1), pages 107-113.
    • Handle: RePEc:taf:uaajxx:v:4:y:2000:i:1:p:107-113
    DOI: 10.1080/10920277.2000.10595885
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    Cited by:

    1. Young, Virginia R., 2000. "Credibility using semiparametric models and a loss function with a constancy penalty," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 151-156, May.
    2. Huang, Xiaowei & Song, Lixin & Liang, Yanchun, 2003. "Semiparametric credibility ratemaking using a piecewise linear prior," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 585-593, December.
    3. Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.

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