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Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

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  • Alai, D. H.
  • Merz, M.
  • Wüthrich, M. V.

Abstract

The prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

Suggested Citation

  • 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, Cambridge University Press, vol. 4(1), pages 7-31, March.
    • Handle: RePEc:cup:anacsi:v:4:y:2009:i:01:p:7-31_00
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    Cited by:

    1. Huang, Jinlong & Wu, Xianyi & Zhou, Xian, 2016. "Asymptotic behaviors of stochastic reserving: Aggregate versus individual models," European Journal of Operational Research, Elsevier, vol. 249(2), pages 657-666.
    2. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    3. Karthik Sriram & Peng Shi, 2021. "Stochastic loss reserving: A new perspective from a Dirichlet model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 195-230, March.
    4. Gian Paolo Clemente & Nino Savelli & Diego Zappa, 2019. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance," International Business Research, Canadian Center of Science and Education, vol. 12(3), pages 123-138, March.
    5. Valandis Elpidorou & Carolin Margraf & María Dolores Martínez-Miranda & Bent Nielsen, 2019. "A Likelihood Approach to Bornhuetter–Ferguson Analysis," Risks, MDPI, vol. 7(4), pages 1-20, December.

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