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Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin

  • Loisel, Stéphane
  • Mazza, Christian
  • Rullière, Didier

We 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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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 42 (2008)
Issue (Month): 2 (April)
Pages: 746-762

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Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:746-762
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  1. Didier Rullière & Stéphane Loisel, 2004. "Another look at the Picard-Lefèvre formula for finite-time ruin probabilities," Post-Print hal-00379412, HAL.
  2. 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.
  3. 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.
  4. Christian Mazza & Didier Rullière, 2004. "A link between wave governed random motions and ruin processes," Post-Print hal-00412977, HAL.
  5. Marceau, Etienne & Rioux, Jacques, 2001. "On robustness in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 167-185, October.
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