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A new approach to the credibility formula

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  • Payandeh Najafabadi, Amir T.

Abstract

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.

Suggested Citation

  • Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 334-338, April.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:334-338
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    References listed on IDEAS

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    1. Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers 92-20, California Irvine - School of Social Sciences.
    2. Roderick M. Rejesus & Keith H. Coble & Thomas O. Knight & Yufei Jin, 2006. "Developing Experience-Based Premium Rate Discounts in Crop Insurance," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(2), pages 409-419.
    3. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 565-600, November.
    4. Landsman, Zinoviy, 2002. "Credibility theory: a new view from the theory of second order optimal statistics," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 351-362, June.
    5. 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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    Cited by:

    1. Najafabadi, Amir T. Payandeh & Bazaz, Ali Panahi, 2018. "An optimal multi-layer reinsurance policy under conditional tail expectation," Annals of Actuarial Science, Cambridge University Press, vol. 12(1), pages 130-146, March.
    2. Payandeh Najafabadi, Amir T. & Hatami, Hamid & Omidi Najafabadi, Maryam, 2012. "A maximum-entropy approach to the linear credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 216-221.
    3. Amir T. Payandeh Najafabadi & Maryam Omidi Najafabadi, 2016. "On the Bayesian estimation for Cronbach's alpha," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2416-2441, October.
    4. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    5. Payandeh Najafabadi, Amir T. & Bazaz, Ali Panahi, 2016. "An optimal co-reinsurance strategy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 149-155.
    6. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2022. "Satisficing credibility for heterogeneous risks," European Journal of Operational Research, Elsevier, vol. 298(2), pages 752-768.
    7. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.

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    More about this item

    Keywords

    IM31 Loss function Balanced loss function Mean square error technique;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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