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Exact Credibility and Tweedie Models

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  • Ohlsson, Esbjörn
  • Johansson, Björn

Abstract

Kaas, Dannenburg & Goovaerts (1997) generalized Jewell’s theorem on exact credibility, from the classical Bühlmann model to the (weighted) Bühlmann-Straub model. We extend this result further to the “Bühlmann-Straub model with a priori differences” (Bühlmann & Gisler, 2005). It turns out that exact credibility holds for a class of Tweedie models, including the Poisson, gamma and compound Poisson distribution – the most important distributions for insurance applications of generalized linear models (GLMs). Our results can also be viewed as an alternative to the HGLM approach for combining credibility and GLMs, see Nelder and Verrall (1997).

Suggested Citation

  • Ohlsson, Esbjörn & Johansson, Björn, 2006. "Exact Credibility and Tweedie Models," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 121-133, May.
    • Handle: RePEc:cup:astinb:v:36:y:2006:i:01:p:121-133_01
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    Cited by:

    1. Martin Eling & Kwangmin Jung, 2022. "Heterogeneity in cyber loss severity and its impact on cyber risk measurement," Risk Management, Palgrave Macmillan, vol. 24(4), pages 273-297, December.
    2. Alicja Wolny-Dominiak & Tomasz Żądło, 2021. "The Measures of Accuracy of Claim Frequency Credibility Predictor," Sustainability, MDPI, vol. 13(21), pages 1-13, October.
    3. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    4. Jeong, Himchan, 2024. "Tweedie multivariate semi-parametric credibility with the exchangeable correlation," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 13-21.

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