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Development Pattern and Prediction Error for the Stochastic Bornhuetter-Ferguson Claims Reserving Method

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  • Saluz, Annina
  • Gisler, Alois
  • Wüthrich, Mario V.

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.

Suggested Citation

  • Saluz, Annina & Gisler, Alois & Wüthrich, Mario V., 2011. "Development Pattern and Prediction Error for the Stochastic Bornhuetter-Ferguson Claims Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 279-313, November.
    • Handle: RePEc:cup:astinb:v:41:y:2011:i:02:p:279-313_00
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    Cited by:

    1. 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.
    2. 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.

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