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A maximum-entropy approach to the linear credibility formula

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  • Payandeh Najafabadi, Amir T.
  • Hatami, Hamid
  • Omidi Najafabadi, Maryam
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    Abstract

    Payandeh [Payandeh Najafabadi, A.T., 2010. A new approach to credibility formula. Insurance: Mathematics and Economy 46, 334–338] introduced a new technique to approximate a Bayes’ estimator with the exact credibility’s form. This article employs a well known and powerful maximum-entropy method (MEM) to extend results of Payandeh Najafabadi (2010) to a class of linear credibility, whenever claim sizes have been distributed according to the logconcave distributions. Namely, (i) it employs the maximum-entropy method to approximate an appropriate Bayes’ estimator (with respect to either the square-error or the Linex loss functions and general increasing and bounded prior distribution) by a linear combination of claim sizes; (ii) it establishes that such an approximation coincides with the exact credibility formula whenever the require conditions for the exact credibility (see below) are held. Some properties of such an approximation are discussed. Application to crop insurance has been given.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 1 ()
    Pages: 216-221

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:216-221

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Linear credibility formula; Bayes’ estimator; Mean square-error technique; Maximum-entropy technique; Panel data; Time series data; Crop insurance;

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    References

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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. 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.
    3. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
    4. 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.
    5. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," MPRA Paper 21587, University Library of Munich, Germany, revised 0020.
    6. Landsman, Zinoviy & Makov, Udi E., 1999. "Credibility evaluation for the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 23-29, March.
    7. Amir H. Darooneh, 2004. "Non-Life Insurance Pricing: Multi Agents Model," Papers cond-mat/0402239, arXiv.org.
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