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Bootstrapping the Separation Method in Claims Reserving

Published online by Cambridge University Press:  09 August 2013

Susanna Björkwall ,
Ola Hössjer  and
Esbjörn Ohlsson
Susanna Björkwall
Affiliation:
Mathematical Statistics, c/o Hössjer, SE-106 91 Stockholm University, E-Mail: [email protected]
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Abstract

The separation method was introduced by Verbeek (1972) in order to forecast numbers of excess claims and it was developed further by Taylor (1977) to be applicable to the average claim cost. The separation method differs from the chain-ladder in that when the chain-ladder only assumes claim proportionality between the development years, the separation method also separates the claim delay distribution from influences affecting the calendar years, e.g. inflation. Since the inflation contributes to the uncertainty in the estimate of the claims reserve it is important to consider its impact in the context of risk management, too.

In this paper we present a method for assessing the prediction error distribution of the separation method. To this end we introduce a parametric framework within the separation model which enables joint resampling of claim counts and claim amounts. As a result, the variability of Taylor's predicted reserves can be assessed by extending the parametric bootstrap techniques of Björkwall et al. (2009). The performance of the bootstrapped separation method and chain-ladder is compared for a real data set.

Keywords

BootstrapChain-ladderDevelopment triangleInflationSeparation methodStochastic claims reserving
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 845 - 869
Copyright
Copyright © International Actuarial Association 2010

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