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Robust Estimation of Reserve Risk

Published online by Cambridge University Press:  09 August 2013

Marc Busse ,
Ulrich Müller  and
Michel Dacorogna
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Abstract

We tackle problems that appear in the practical application of the Mack method for the estimation of reserving risk and the bootstrapping of ultimate reserve distributions. More specifically, we design a filter for outliers and large jumps, and present a robust version of Mack's variance estimator. A combination of these guarantees a reasonable Mack and bootstrap error even for deficient data. Furthermore, a method is derived that allows us to remove the influence of fluctuations in earning patterns from the reserve risk estimate. It is thereby shown that the relation between underwriting and accident year based loss development patterns is given by a convolution. A numerically stable inversion thereof is obtained by means of a Tikhonov regularization. The reliability of the presented methods is verified with several loss triangles.

Keywords

Reserve riskstochastic reservesdynamic financial analysisMack methodbootstraprobust statisticsTikhonov regularizationinverse problems
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 453 - 489
Copyright
Copyright © International Actuarial Association 2010

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