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Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models

Published online by Cambridge University Press:  09 August 2013

Gareth W. Peters ,
Pavel V. Shevchenko  and
Mario V. Wüthrich
Gareth W. Peters
Affiliation:
CSIRO Mathematical and Information Sciences, Sydney, Locked Bag 17, North Ryde, NSW, 1670, Australia UNSW Mathematics and Statistics Department, Sydney, 2052, Australia., E-Mail: peterga@maths.unsw.edu.au
Mario V. Wüthrich
Affiliation:
ETH Zurich, Department of Mathematics, CH-8092 Zurich, Switzerland., E-Mail: wueth@math.ethz.ch
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Abstract

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

Keywords

Claims reservingmodel uncertaintyTweedie's compound Poisson modelBayesian analysismodel selectionmodel averagingMarkov chain Monte Carlo
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 1 - 33
Copyright
Copyright © International Actuarial Association 2009

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