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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.

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File URL: http://mpra.ub.uni-muenchen.de/21587/
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 21587.

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Date of creation: 2010
Date of revision: 0020
Handle: RePEc:pra:mprapa:21587

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Keywords: Loss function Balanced loss function Mean square error technique;

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  1. 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.
  2. Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers, California Irvine - School of Social Sciences 92-20, California Irvine - School of Social Sciences.
  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.
  4. 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, Agricultural and Applied Economics Association, vol. 88(2), pages 409-419.
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Cited by:
  1. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
  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.

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