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

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

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Stéphane Loisel () (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - Université Claude Bernard - Lyon I)
Christian Mazza () (Département de Mathématiques - Université de Fribourg)
Didier Rullière () (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - Université Claude Bernard - Lyon I)

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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.

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Paper provided by HAL in its series Pre- and Post-Print documents with number hal-00168714_v1.

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Date of creation: 2006
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Handle: RePEc:hal:papers:hal-00168714_v1

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This paper has been announced in the following NEP Reports:

NEP-ALL-2007-09-16 (All new papers)
NEP-ECM-2007-09-16 (Econometrics)
NEP-RMG-2007-09-16 (Risk Management)

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Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Pre- and Post-Print documents hal-00168958_v1, HAL. [Downloadable!]
Stéphane Loisel & Christian Mazza & Didier Rullière, 2007. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Pre- and Post-Print documents hal-00168716_v1, HAL. [Downloadable!]

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This page was last updated on 2008-6-15.

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