A new approach to the credibility formula

Payandeh Najafabadi, Amir T. (2010): A new approach to the credibility formula. Published in: Insurance: Mathematics and Economics No. 46 (2010): pp. 334-338.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Loss function Balanced loss function Mean square error technique
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Statistical Decision Theory; Operations Research; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C11 - Bayesian Analysis

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