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Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution

Published online by Cambridge University Press:  17 April 2015

Jennifer S.K. Chan ,
S.T. Boris Choy  and
Udi E. Makov
Jennifer S.K. Chan
Affiliation:
School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia, E-Mail: jchan@maths.usyd.edu.au
S.T. Boris Choy
Affiliation:
Department of Mathematical Sciences, University of Technology Sydney, P.O. Box 123, Broadway, NSW 2007, Australia, E-Mail: boris.choy@uts.edu.au
Udi E. Makov
Affiliation:
Department of Statistics, University of Haifa, Haifa, 31905 Israel, E-Mail: makov@stat.haifa.ac.il
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Abstract

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This paper presents a Bayesian approach using Markov chain Monte Carlo methods and the generalized-t (GT) distribution to predict loss reserves for the insurance companies. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserves. To develop a more robust model for irregular claims, this paper extends the conventional normal error distribution to the GT distribution which nests several heavy-tailed distributions including the Student-t and exponential power distributions. It is shown that the GT distribution can be expressed as a scale mixture of uniforms (SMU) distribution which facilitates model implementation and detection of outliers by using mixing parameters. Different models for the mean function, including the log-ANOVA, log-ANCOVA, state space and threshold models, are adopted to analyze real loss reserves data. Finally, the best model is selected according to the deviance information criterion (DIC).

Keywords

Bayesian approachstate space modelthreshold modelscale mixtures of uniform distributiondeviance information criterion
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 207 - 230
Copyright
Copyright © ASTIN Bulletin 2008

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