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Asymptotic theory for Mack's model

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  • Steinmetz, Julia
  • Jentsch, Carsten

Abstract

The distribution-free chain ladder reserving model by Mack (1993) belongs to the most popular approaches in non-life insurance mathematics. It was originally proposed to determine the first two moments of the reserve distribution. Together with a normal approximation, it is commonly applied to conduct statistical inference including the estimation of large quantiles of the reserve and determination of the reserve risk. However, for Mack's model, the literature lacks a rigorous justification of such a normal approximation for the reserve.

Suggested Citation

  • Steinmetz, Julia & Jentsch, Carsten, 2022. "Asymptotic theory for Mack's model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 223-268.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:223-268
    DOI: 10.1016/j.insmatheco.2022.08.007
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    References listed on IDEAS

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    1. Jonas Harnau & Bent Nielsen, 2018. "Over-Dispersed Age-Period-Cohort Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1722-1732, October.
    2. 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.
    3. Buchwalder, Markus & Bühlmann, Hans & Merz, Michael & Wüthrich, Mario V., 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 521-542, November.
    4. 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.
    5. Mack, Thomas & Quarg, Gerhard & Braun, Christian, 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 543-552, November.
    6. 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.
    7. Buchwalder, Markus & Bühlmann, Hans & Merz, Michael & Wüthrich, Mario V., 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method – Final Remark," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 553-553, November.
    8. Gisler, Alois, 2019. "The Reserve Uncertainties In The Chain Ladder Model Of Mack Revisited," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 787-821, September.
    9. Lindholm, Mathias & Lindskog, Filip & Wahl, Felix, 2020. "Estimation of conditional mean squared error of prediction for claims reserving," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 93-128, March.
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    Cited by:

    1. 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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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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