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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: esbjorn.ohlsson@math.su.se
Björn Johansson
Affiliation:
Länsförsäkringar Alliance, SE-106 50 Stockholm, Sweden, E-mail: bjorn.johansson@lansforsakringar.se
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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

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