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

Stéphane Loisel (), Christian Mazza () and Didier Rulliere ()
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Christian Mazza: Département de Mathématiques - Albert-Ludwigs-Universität Freiburg

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Abstract: 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.

Keywords: Finite-time ruin probability; robustness; Solvency II; reliable ruin probability; asymptotic Normality; influence function; Estimation Risk Solvency Margin (ERSM) (search for similar items in EconPapers)
Date: 2008-04
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00168714
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Published in Insurance Mathematics and Economics, 2008, 42 (2), pp.746-762. ⟨10.1016/j.insmatheco.2007.08.007⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00168714

DOI: 10.1016/j.insmatheco.2007.08.007

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