Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-11T02:36:01.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited

Published online by Cambridge University Press:  21 October 2010

D. H. Alai ,
M. Merz  and
M. V. Wüthrich
Get access Rights & Permissions [Opens in a new window]

Abstract

We revisit the stochastic model of Alai et al. (2009) for the Bornhuetter-Ferguson claims reserving method, Bornhuetter & Ferguson (1972). We derive an estimator of its conditional mean square error of prediction (MSEP) using an approach that is based on generalized linear models and maximum likelihood estimators for the model parameters. This approach leads to simple formulas, which can easily be implemented in a spreadsheet.

Keywords

Claims ReservingBornhuetter-FergusonOverdispersed Poisson DistributionChain Ladder MethodGeneralized Linear ModelsFisher Information MatrixConditional Mean Square Error of Prediction
Type
Papers
Information
Annals of Actuarial Science , Volume 5 , Issue 1 , March 2011 , pp. 7 - 17
Copyright
Copyright © Institute and Faculty of Actuaries 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alai, D. H., Merz, M., Wüthrich, M. V. (2009). Mean square error of prediction in the Bornhuetter-Ferguson claims reserving method. Annals of Actuarial Science, 4, 7–31.CrossRefGoogle Scholar
Bornhuetter, R. L., Ferguson, R. E. (1972). The actuary and IBNR. Proceedings CAS, LIX, 181–195.Google Scholar
Buchwalder, M., Bühlmann, H., Merz, M., Wüthrich, M. V. (2006). The mean square error of prediction in the chain ladder reserving method (Mack and Murphy revisited). ASTIN Bulletin, 36(2), 543–571.Google Scholar
England, P. D., Verrall, R. J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–518.Google Scholar
Hachemeister, C., Stanard, J. (1975). IBNR claims count estimation with static lag functions. Presented at ASTIN Colloquium, Portimao, Portugal.Google Scholar
Kuang, D., Nielsen, B., Nielsen, J. P. (2008a). Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika, 95(4), 987–991.CrossRefGoogle Scholar
Kuang, D., Nielsen, B., Nielsen, J. P. (2008b). Identification of the age-period-cohort model and the extended chain-ladder model. Biometrika, 95(4), 979–986.CrossRefGoogle Scholar
Kuang, D., Nielsen, B., Nielsen, J. P. (2009). Chain-Ladder as maximum likelihood revisited. Annals of Actuarial Science, 4, 105–121.CrossRefGoogle Scholar
Lehmann, E. L. (1983). Theory of Point Estimation. Wiley & Sons, New York.CrossRefGoogle Scholar
Mack, T. (1991). A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 21(1), 93–109.CrossRefGoogle Scholar
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserves estimates. ASTIN Bulletin, 23(2), 213–225.CrossRefGoogle Scholar
Mack, T. (2008). The prediction error of Bornhuetter/Ferguson. ASTIN Bulletin, 38(1), 87–103.CrossRefGoogle Scholar
Neuhaus, W. (1992). Another pragmatic loss reserving method or Bornhuetter/Ferguson revisited. Scandinavian Actuarial Journal, 2, 151–162.CrossRefGoogle Scholar
Schmidt, K. D., Zocher, M. (2008). The Bornhuetter-Ferguson principle. Variance, 2(1), 85–110.Google Scholar
Verrall, R. J. (2004). A Bayesian generalized linear model for the Bornhuetter-Ferguson method of claims reserving. North American Actuarial Journal, 8(3), 67–89.CrossRefGoogle Scholar
Wüthrich, M. V., Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance. Wiley & Sons, West Sussex.Google Scholar