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

Author

Listed:
  • Alexandre Boumezoued

    (R&D, Milliman, Paris - Milliman France)

  • Yoboua Angoua

    (R&D, Milliman, Paris - Milliman France)

  • Laurent Devineau

    (R&D Milliman - Milliman France, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Jean-Philippe Boisseau

    (R&D, Milliman, Paris - Milliman France)

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 Wüthrich 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," Working Papers hal-00605329, HAL.
    • Handle: RePEc:hal:wpaper:hal-00605329
    Note: View the original document on HAL open archive server: https://hal.science/hal-00605329v2
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    References listed on IDEAS

    as
    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. 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.
    4. 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.
    5. David Scollnik, 2001. "Actuarial Modeling with MCMC and BUGs," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 96-124.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Non‐life insurance; Reserve risk; Claims Development Result; Bootstrap method; Tail factor; Prediction error; Solvency II;
    All these keywords.

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