A new approach to the credibility formula
AbstractThe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 46 (2010)
Issue (Month): 2 (April)
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Web page: http://www.elsevier.com/locate/inca/505554
IM31 Loss function Balanced loss function Mean square error technique;
Other versions of this item:
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers 92-20, California Irvine - School of Social Sciences.
- 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.
- Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
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