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One-year reserve risk including a tail factor: closed formula and bootstrap approaches

Author

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  • Alexandre Boumezoued

    (SAF)

  • Yoboua Angoua

    (SAF)

  • Laurent Devineau

    (SAF)

  • Jean-Philippe Boisseau

Abstract

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by W\"uthrich et al. (2008). In particular, we integrate the stochastic modeling of a tail factor in the bootstrap procedure. We demonstrate the equivalence with existing analytical results and develop closed-form expressions for the error of prediction including a tail factor. A numerical example is given at the end of this study.

Suggested Citation

  • Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Papers 1107.0164, arXiv.org, revised Apr 2012.
    • Handle: RePEc:arx:papers:1107.0164
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. David Scollnik, 2001. "Actuarial Modeling with MCMC and BUGs," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 96-124.
    4. England, Peter, 2002. "Addendum to "Analytic and bootstrap estimates of prediction errors in claims reserving"," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 461-466, December.
    5. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 221-270, September.
    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.
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    Cited by:

    1. Geoffrey Nichil & Pierre Vallois, 2019. "Solvency Need Resulting from Reserving Risk in a ORSA Context," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 567-592, June.

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