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Exact Credibility and Tweedie Models

Published online by Cambridge University Press:  17 April 2015

Esbjörn Ohlsson  and
Björn Johansson
Esbjörn Ohlsson
Affiliation:
Mathematical Statistics, Department of Mathematics Stockholm University, SE-106 91 Stockholm, Sweden, E-mail: [email protected]
Björn Johansson
Affiliation:
Länsförsäkringar Alliance, SE-106 50 Stockholm, Sweden, E-mail: [email protected]
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Abstract

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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).

Keywords

Credibility theorya priori differencesJewell’s theoremgeneralized linear modelsTweedie models
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 121 - 133
Copyright
Copyright © ASTIN Bulletin 2006

References

Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin, 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications. Springer-Verlag, Berlin.Google Scholar
Goovaerts, M.J. and Hoogstad, W.J. (1987) Credibility Theory. Survey of Actuarial Studies No. 4, Nationale-Nederlanden N.V.Google Scholar
Jewell, W.S. (1974) Credible means are exact Bayesian for exponential families. ASTIN Bulletin, 8, 77–90.CrossRefGoogle Scholar
Jørgensen, B. (1997) The Theory of Dispersion Models. Chapman and Hall, London.Google Scholar
Jørgensen, B. and Paes De Souza, M.C. (1994) Fitting Tweedie’s compound Poisson model to insurance claim data. Scand. Actuarial Journal, 69–93.CrossRefGoogle Scholar
Kaas, R., Dannenburg, D. and Goovaerts, M.J. (1997) Exact credibility for weighted observations. ASTIN Bulletin, 27, 287–295.CrossRefGoogle Scholar
Kaas, R., Goovaerts, M.J., Dhaene, J. and Denuit, M. (2001) Modern Actuarial Risk Theory. Kluwer Academic Publishers, Dordrecht.Google Scholar
Lee, Y. and Nelder, J.A. (1996) Hierarchical Generalized linear models. J.R. Statist. Soc. B, 58(4), 619–678.Google Scholar
Nelder, J.A. and Verrall, R.J. (1997) Credibility Theory and Generalized linear models. ASTIN Bulletin, 27(1), 71–82.CrossRefGoogle Scholar
Ohlsson, E. (2004) Credibility Rating in a Multiplicative Tariff. Paper presented at the 35th ASTIN Colloquium, http://www.astin2004.no/.Google Scholar
Ohlsson, E. and Johansson, B. (2004) Combining Credibility and GLM for Rating of Multi-Level Factors. CAS 2004 Discussion Paper Program, http://www.casact.org/pubs/dpp/dpp04/.Google Scholar
Renshaw, A.E. (1994) Modeling the claims process in the precense of covariates. ASTIN Bulletin, 24(2), 265–285.CrossRefGoogle Scholar