Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin
AbstractWe consider the classical risk model and carry out a sensitivity and robustness analysis of finite-time ruin probabilities. We provide algorithms to compute the related influence functions. We also prove the weak convergence of a sequence of empirical finite-time ruin probabilities starting from zero initial reserve toward a Gaussian random variable. We define the concepts of reliable finite-time ruin probability as a Value-at-Risk of the estimator of the finite-time ruin probability. To control this robust risk measure, an additional initial reserve is needed and called Estimation Risk Solvency Margin (ERSM). We apply our results to show how portfolio experience could be rewarded by cut-offs in solvency capital requirements. An application to catastrophe contamination and numerical examples are also developed.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 42 (2008)
Issue (Month): 2 (April)
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Web page: http://www.elsevier.com/locate/inca/505554
Other versions of this item:
- 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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
- Marceau, Etienne & Rioux, Jacques, 2001. "On robustness in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 167-185, October.
- Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
- Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
- Croux, Kristof & Veraverbeke, Noel, 1990. "Nonparametric estimators for the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 127-130, September.
- 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.
- 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.
- Stéphane Loisel & Nicolas Privault, 2009. "Sensitivity analysis and density estimation for finite-time ruin probabilities," Post-Print hal-00201347, HAL.
- 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.
- Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
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