A new approach to the credibility formula
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.
|Date of creation:||2010|
|Date of revision:||0020|
|Publication status:||Published in Insurance: Mathematics and Economics 46 (2010): pp. 334-338|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers 92-20, California Irvine - School of Social Sciences.
- 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.
- Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 565-600, November.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:21587. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.