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A maximum-entropy approach to the linear credibility formula

Author

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

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:216-221
    DOI: 10.1016/j.insmatheco.2011.08.010
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    References listed on IDEAS

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    1. Amir H. Darooneh, 2004. "Non-Life Insurance Pricing: Multi Agents Model," Papers cond-mat/0402239, arXiv.org.
    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.
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    4. 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.
    5. Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    6. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    7. 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.
    8. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 334-338, April.
    9. 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.
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    Cited by:

    1. Najafabadi, Amir T. Payandeh & Bazaz, Ali Panahi, 2018. "An optimal multi-layer reinsurance policy under conditional tail expectation," Annals of Actuarial Science, Cambridge University Press, vol. 12(1), pages 130-146, March.
    2. Minwoo Kim & Himchan Jeong & Dipak Dey, 2022. "Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach," Risks, MDPI, vol. 10(3), pages 1-11, March.
    3. Payandeh Najafabadi, Amir T. & Bazaz, Ali Panahi, 2016. "An optimal co-reinsurance strategy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 149-155.

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    More about this item

    Keywords

    Linear credibility formula; Bayes’ estimator; Mean square-error technique; Maximum-entropy technique; Panel data; Time series data; Crop insurance;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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