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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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    1. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    5. 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.
    6. 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.
    7. Payandeh Najafabadi, Amir T. & Bazaz, Ali Panahi, 2016. "An optimal co-reinsurance strategy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 149-155.

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    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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