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On Comparison of Stochastic Reserving Methods with Bootstrapping

Author

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  • Liivika Tee

    (Institute of Mathematics and Statistics, Faculty of Science and Technology, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia)

  • Meelis Käärik

    (Institute of Mathematics and Statistics, Faculty of Science and Technology, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia)

  • Rauno Viin

    (Institute of Mathematics and Statistics, Faculty of Science and Technology, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia)

Abstract

We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping framework, we discuss the choice of residuals, namely the Pearson residuals, the deviance residuals and the Anscombe residuals. In addition, several possible residual adjustments are discussed and compared in a case study. We carry out a practical implementation and comparison of methods using real-life insurance data to estimate reserves and their prediction errors. We propose to consider proper scoring rules for model validation, and the assessments will be drawn from an extensive case study.

Suggested Citation

  • Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
  • Handle: RePEc:gam:jrisks:v:5:y:2017:i:1:p:2-:d:86840
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    References listed on IDEAS

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    1. Haastrup, Svend & Arjas, Elja, 1996. "Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 139-164, November.
    2. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    3. Mack, Thomas, 1991. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 93-109, April.
    4. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
    5. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    6. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, October.
    7. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Identification of the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 979-986.
    8. Schmidt, Klaus D., 2002. "A note on the overdispersed Poisson family," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 21-25, February.
    9. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    10. Renshaw, A.E. & Verrall, R.J., 1998. "A Stochastic Model Underlying the Chain-Ladder Technique," British Actuarial Journal, Cambridge University Press, vol. 4(4), pages 903-923, October.
    11. D. Kuang & B. Nielsen & J. P. Nielsen, 2009. "Chain-Ladder as Maximum Likelihood Revisited," Economics Papers 2009-W08, Economics Group, Nuffield College, University of Oxford.
    12. Ashe, Frank, 1986. "An Essay at Measuring the Variance of Estimates of Outstanding Claim Payments," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 99-113, April.
    13. Verrall, R. J., 2000. "An investigation into stochastic claims reserving models and the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 91-99, February.
    14. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
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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. Steinmetz, Julia & Jentsch, Carsten, 2024. "Bootstrap consistency for the Mack bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 83-121.

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