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Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes

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  • Stéphane Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

The classical risk model is considered and a sensitivity analysis of finite-time ruin probabilities is carried out. We prove the weak convergence of a sequence of empirical finite-time ruin probabilities. So-called partly shifted risk processes are introduced, and used to derive an explicit expression of the asymptotic variance of the considered estimator. This provides a clear representation of the influence function associated with finite time ruin probabilities, giving a useful tool to quantify estimation risk according to new regulations.
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Suggested Citation

  • Stéphane Loisel, 2007. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Post-Print hal-00397269, HAL.
    • Handle: RePEc:hal:journl:hal-00397269
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    Cited by:

    1. Stéphane Loisel & Nicolas Privault, 2009. "Sensitivity analysis and density estimation for finite-time ruin probabilities," Post-Print hal-00201347, HAL.
    2. Fabrice Borel-Mathurin & Nicole El Karoui & Stéphane Loisel & Julien Vedani, 2020. "Locality in time of the European insurance regulation "risk-neutral" valuation framework, a pre-and post-Covid analysis and further developments," Working Papers hal-02905181, HAL.
    3. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.
    4. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.

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