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

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  • Alexandre Boumezoued

    (SAF)

  • Yoboua Angoua

    (SAF)

  • Laurent Devineau

    (SAF)

  • Jean-Philippe Boisseau
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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 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.

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    File URL: http://arxiv.org/pdf/1107.0164
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1107.0164.

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    Date of creation: Jul 2011
    Date of revision: Apr 2012
    Handle: RePEc:arx:papers:1107.0164

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    Web page: http://arxiv.org/

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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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