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Sensitivity analysis and density estimation for finite-time ruin probabilities

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Author Info

  • Stéphane Loisel

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Nicolas Privault

    ()
    (Department of Mathematics - City University of 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.

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File URL: http://hal.archives-ouvertes.fr/docs/00/26/88/00/PDF/Loisel-Privault-ISFA-WP2041-v2.pdf
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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00201347.

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Date of creation: 2009
Date of revision:
Publication status: Published, Journal of Computational and Applied Mathematics, 2009, 230, 1, 107-120
Handle: RePEc:hal:journl:hal-00201347

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00201347/en/
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Related research

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

This paper has been announced in the following NEP Reports:

References

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  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. Stéphane Loisel & Christian Mazza & Didier Rullière, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Post-Print hal-00168714, HAL.
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Cited by:
  1. 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.
  2. Stéphane Loisel & Christian Mazza & Didier Rullière, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Post-Print hal-00168716, HAL.

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