No CrossRef data available.
Article contents
Development Pattern and Prediction Error for the Stochastic Bornhuetter-Ferguson Claims Reserving Method
Published online by Cambridge University Press: 09 August 2013
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
- Type
- Research Article
- Information
- Copyright
- Copyright © International Actuarial Association 2011
References
[1] Alai, D.H. and Wüthrich, M.V. ((2009) Taylor approximations for model uncertainty within the Tweedie exponential dispersion family. ASTIN Bulletin
39(2), 453–478.CrossRefGoogle Scholar
[2] Alai, D.H., Merz, M. and Wüthrich, M.V. (2010) Prediction uncertainty in the Bornhuetter-Ferguson claims reserving method: revisited. Annals of Actuarial Science
5(1), 7–17.CrossRefGoogle Scholar
[3] Bornhuetter, R.L. and Ferguson, R.E. (1972) The actuary and IBNR. Proc. CAS, LIX, 181–195.Google Scholar
[4] Bühlmann, H. and Straub, E. (1983) Estimation of IBNR reserves by the methods chain ladder, Cape Cod and complementary loss ratio. International Summer School 1983, unpublished.Google Scholar
[5] England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal
8(3), 443–518.CrossRefGoogle Scholar
[6] Hachemeister, C. and Stanard, J. (1975) IBNR claims count estimation with static lag functions. Presented at ASTIN Colloquium, Portimao, Portugal.Google Scholar
[7] Mack, T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin
21(1), 93–109.CrossRefGoogle Scholar
[8] Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin
23(2), 213–225.CrossRefGoogle Scholar
[9] Mack, T. (2008) The prediction error of Bornhuetter/Ferguson. ASTIN Bulletin
38(1), 87–103.CrossRefGoogle Scholar
[10] Neuhaus, W. (1992) Another pragmatic loss reserving method or Bornhuetter/Ferguson revisited. Scand. Actuarial J.
2, 151–162.CrossRefGoogle Scholar
[11] Radtke, M. and Schmidt, K.D. (2004) Handbuch zur Schadenreservierung. Karlsruhe: Verlag Versicherungswirtschaft S.
47ff.Google Scholar
[12] Schmidt, K.D. and Wünsche, A. (1998) Chain ladder, marginal sum and maximum likelihood estimation. Blätter DGVM
23(3), 267–277.CrossRefGoogle Scholar
[13] Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley Finance.Google Scholar