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

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Author Info

  • Alexandre Boumezoued

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

  • Yoboua Angoua

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

  • Laurent Devineau

    ()
    (R&D Milliman - Milliman, SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Jean-Philippe Boisseau

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

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    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.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/68/45/94/PDF/One_Year_Reserve_Risk_Tail_Factor_v2.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00605329.

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    Date of creation: 01 Jul 2011
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    Handle: RePEc:hal:wpaper:hal-00605329

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00605329
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    Related research

    Keywords: Non‐life insurance; Reserve risk; Claims Development Result; Bootstrap method; Tail factor; Prediction error; Solvency II;

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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. 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.
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