Claims Reserving in Non-life Insurance: A Fully Bayesian Model

  • Gilberto Castellani
  • Massimo De Felice
  • Franco Moriconi
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


Stochastic claims reserving has been developed mostly using models defined in the framework of the classical statistics. The recently proposed Time Series Chain Ladder (TSCL) is one of these models. In order to allow for a comparison with the Bayesian point of view, we propose a fully Bayesian model having the property of reproducing TSCL if improper priors are assumed. With “informative” priors the Bayesian model allows for incorporating into the reserving process relevant external data, e.g. expert opinions, which are largely used by the actuaries. We provide numerical examples using Markov Chain Monte Carlo methods.


Claims reserving Chain Ladder Reserve Risk Bayesian modelling Markov Chain Monte Carlo Solvency II 


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  1. 1.
    Buchwalder, M., Bühlmann, H., Merz, M., Wüthrich, M.V.: The mean square error of prediction in the chain ladder reserving method (Mack and Murphy revisited). ASTIN Bulletin 36, 521–542 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    de Finetti, B.: Theory of Probability. A critical introductory treatment. Wiley, New York (1975)zbMATHGoogle Scholar
  3. 3.
    Gisler, A.: The Estimation Error in the Classical Chain-Ladder Reserving Method: a Bayesian Approach. ASTIN Bulletin 36, 554–565 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Gisler, A., Wüthrich, M.V.: Credibility for the Chain Ladder Method. ASTIN Bulletin 38, 565–600 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Mack, T.: Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23, 213–225 (1993)CrossRefGoogle Scholar
  6. 6.
    Salzmann, R., Wüthrich, M.V., Merz, M.: Higher Moments of the Claims Development Result in General Insurance (preprint) (to appear in ASTIN Bulletin) (2010)Google Scholar
  7. 7.
    Wüthrich, M.V., Merz, M.: Stochastic Claims Reserving Methods in Insurance. Wiley, New York (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gilberto Castellani
    • 1
  • Massimo De Felice
    • 1
  • Franco Moriconi
    • 2
  1. 1.Dip. di Scienze StatisticheSapienza, Università di RomaRomeItaly
  2. 2.Dip. di Economia, Finanza e StatisticaUniversità di PerugiaPerugiaItaly

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