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Sensitivity analysis and density estimation for finite-time ruin probabilities

Author

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  • Stéphane Loisel

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

  • Nicolas Privault

    () (Department of Mathematics - CUHK - City University of Hong Kong [Hong Kong])

Abstract

The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly non-continuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these representation formulas perform better than standard finite difference methods. Our approach differs from standard Malliavin probabilistic representation techniques which generally require more smoothness on random variables, entailing the continuity of their density functions.

Suggested Citation

  • Stéphane Loisel & Nicolas Privault, 2009. "Sensitivity analysis and density estimation for finite-time ruin probabilities," Post-Print hal-00201347, HAL.
  • Handle: RePEc:hal:journl:hal-00201347
    DOI: 10.1016/j.cam.2008.10.066
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00201347v3
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    File URL: https://hal.archives-ouvertes.fr/hal-00201347v3/document
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    References listed on IDEAS

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    1. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 746-762, April.
    2. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 374-381, December.
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    Cited by:

    1. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 374-381, December.
    2. 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.

    More about this item

    Keywords

    Ruin probability; Malliavin calculus; insurance; integration by parts;

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