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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: sbj@student.su.se
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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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References

Björkwall, S., Hössjer, O. and Ohlsson, E. (2009) Non-parametric and Parametric Bootstrap Techniques for Age- to-Age Development Factor Methods in Stochastic Claims Reserving. Scandinavian Actuarial Journal, 4, 306–331.Google Scholar
Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M. (2006) The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy revisited). Astin Bulletin, 36(2), 521–542.Google Scholar
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and their Applications. Cambridge University Press.Google Scholar
England, P. (2002) Addendum to “Analytic and Bootstrap Estimates of Prediction Error in Claims Reserving”. Insurance: Mathematics and Economics, 31, 461–466.Google Scholar
England, P. and Verrall, R. (1999) Analytic and Bootstrap Estimates of Prediction Errors in Claims Reserving. Insurance: Mathematics and Economics, 25, 281–293.Google Scholar
Jørgensen, B. and De Souza, M.C.P. (1994) Fitting Tweedie's Compound Poisson Model to Insurance Claims Data. Scandinavian Actuarial Journal, 1, 69–93.CrossRefGoogle Scholar
Li, J. (2006) Comparison of Stochastic Reserving Methods. Australian Actuarial Journal, 12(4), 489–569.Google Scholar
Liu, H. and Verrall, R. (2008) Bootstrap Estimation of the Predictive Distributions of Reserves Using Paid and Incurred Claims. ASTIN Colloquium, Manchester 2008. Available online at: http://www.actuaries.org/ASTIN/Colloquia/Manchester/Papers_EN.cfm Google Scholar
Mack, T. (1993) Distribution Free Calculation of the Standard Error of Chain Ladder Reserve Estimates. Astin Bulletin, 23(2), 213–225.Google Scholar
Mack, T. (2008) The Prediction Error of Bornhuetter/Ferguson. Astin Bulletin, 38(1), 87–103.Google Scholar
Mack, T., Quarg, G. and Braun, C. (2006) The Mean Square Error of Prediction in the Chain Ladder Reserving Method – a Comment. Astin Bulletin, 36(2), 543–552.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models. London: Chapman and Hall.Google Scholar
Pinheiro, P.J.R., Andrade e Silva, J.M. and Centeno, M.d.L (2003) Bootstrap Methodology in Claim Reserving. The Journal of Risk and Insurance, 4, 701–714.CrossRefGoogle Scholar
Quarg, G. and Mack, T. (2004) Munich Chain Ladder. Blätter der DGVFM, 26, 597–630.Google Scholar
Renshaw, A.E. (1994) Modelling the Claims Process in the Presence of Covariates. Astin Bulletin, 24, 265–286.Google Scholar
Smyth, G.K. and Jørgensen, B. (2002) Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling. Astin Bulletin, 32, 143–157.CrossRefGoogle Scholar
Taylor, G. (2000) Loss Reserving – An Actuarial Perspective. Boston: Kluwer Academic Press.Google Scholar
Taylor, G. (1977) Separation of Inflation and Other Effects from the Distribution of Non-life Insurance Claims Delays. Astin Bulletin, 9, 217–230.Google Scholar
Taylor, G. and Ashe, F.R. (1983) Second Moments of Estimates of Outstanding Claims. Journal of Econometrics, 23, 37–61.Google Scholar
Verbeek, H.G. (1972) An Approach to the Analysis of Claims Experience in Motor Liability Excess of Loss Reassurance. Astin Bulletin, 6, 195–202.Google Scholar