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Development Pattern and Prediction Error for the Stochastic Bornhuetter-Ferguson Claims Reserving Method

Published online by Cambridge University Press:  09 August 2013

Annina Saluz ,
Alois Gisler  and
Mario V. Wüthrich
Annina Saluz
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
Alois Gisler
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
Mario V. Wüthrich
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
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Abstract

We investigate the question how the development pattern in the Bornhuetter-Ferguson method should be estimated and derive the corresponding conditional mean square error of prediction (MSEP) of the ultimate claim prediction. An estimator of this conditional MSEP in a distribution-free model was given by Mack [9], whereas in Alai et al. [2] this conditional MSEP was studied in an over-dispersed Poisson model using the chain ladder development pattern. First we consider distributional models and derive estimators (maximum likelihood) for the development pattern taking all relevant information into account. Moreover, we suggest new estimators of the correlation matrix of these estimators and new estimators of the conditional MSEP. Our findings supplement some of Mack's results. The methodology is illustrated at two numerical examples.

Keywords

Claims ReservingBornhuetter-Ferguson MethodMean Square Error of PredictionClaims Development Pattern
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 2 , November 2011 , pp. 279 - 313
Copyright
Copyright © International Actuarial Association 2011

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References

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