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Bootstrap Methodology in Claim Reserving

Author

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  • Paulo J. R. Pinheiro
  • João Manuel Andrade e Silva
  • Maria De Lourdes Centeno

Abstract

In this article, we use the bootstrap technique to obtain prediction errors for different claim‐reserving methods, namely, the chain ladder technique and methods based on generalized linear models. We discuss several forms of performing the bootstrap and illustrate the different solutions using the data set from Taylor and Ashe (1983), which has already been used by several authors.

Suggested Citation

  • Paulo J. R. Pinheiro & João Manuel Andrade e Silva & Maria De Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714, December.
    • Handle: RePEc:bla:jrinsu:v:70:y:2003:i:4:p:701-714
    DOI: 10.1046/j.0022-4367.2003.00071.x
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    References listed on IDEAS

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    1. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    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, 1994. "Which stochastic model is underlying the chain ladder method?," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 133-138, December.
    4. Mack, Thomas & Venter, Gary, 2000. "A comparison of stochastic models that reproduce chain ladder reserve estimates," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 101-107, February.
    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. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    7. Moulton, Lawrence H. & Zeger, Scott L., 1991. "Bootstrapping generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 53-63, January.
    8. 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.
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    Citations

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    Cited by:

    1. Apaydin, Aysen & Baser, Furkan, 2010. "Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 113-122, October.
    2. Benjamin Avanzi & Xingyun Tan & Greg Taylor & Bernard Wong, 2023. "Cyber Insurance Risk: Reporting Delays, Third-Party Cyber Events, and Changes in Reporting Propensity -- An Analysis Using Data Breaches Published by U.S. State Attorneys General," Papers 2310.04786, arXiv.org.
    3. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    4. Álvarez-Jareño, José Antonio & Coll-Serrano, Vicente, 2012. "Estimación de reservas en una compañía aseguradora. Una aplicación en Excel del método Chain-Ladder y Bootstrap || Estimating the Reserves in Insurance Companies: An Excel Application of the Chain-Lad," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 14(1), pages 124-136, December.
    5. 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.
    6. László Martinek, 2019. "Analysis of Stochastic Reserving Models By Means of NAIC Claims Data," Risks, MDPI, vol. 7(2), pages 1-27, June.
    7. Afaf Antar Zohry & Mostafa Abdelghany Ahmed, 2021. "The Prediction Error of the Chain Ladder Method (With Application to Real Data)," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 12(12), pages 1-14, December.
    8. J. Harnau & B. Nielsen, 2017. "Over-dispersed age-period-cohort models," Economics Papers 2017-W06, Economics Group, Nuffield College, University of Oxford.
    9. de Alba, Enrique & Nieto-Barajas, Luis E., 2008. "Claims reserving: A correlated Bayesian model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 368-376, December.
    10. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    11. Fröhlich, Andreas & Weng, Annegret, 2018. "Parameter uncertainty and reserve risk under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 130-141.
    12. Klaus Schmidt, 2012. "Loss prediction based on run-off triangles," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 265-310, June.
    13. Wahl, Felix & Lindholm, Mathias & Verrall, Richard, 2019. "The collective reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 34-50.
    14. Verdonck, T. & Debruyne, M., 2011. "The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 85-98, January.
    15. 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.
    16. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
    17. Andreas Frohlich & Annegret Weng, 2016. "Parameter uncertainty and reserve risk under Solvency II," Papers 1612.03066, arXiv.org, revised Apr 2017.

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