Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes.

Abstract : The classical risk model is considered and a sensitivity analysis of finite-time ruin probabilities is carried out. We prove the weak convergence of a sequence of empirical finite-time ruin probabilities. So-called partly shifted risk processes are introduced, and used to derive an explicit expression of the asymptotic variance of the considered estimator. This provides a clear representation of the influence function associated with finite time ruin probabilities, giving a useful tool to quantify estimation risk according to new regulations.
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Stéphane Loisel, Christian Mazza, Didier Rullière. Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes.. Insurance Mathematics and Economics, 2009, 45 (3), pp.374-381. ⟨10.1016/j.insmatheco.2009.08.003⟩. ⟨hal-00168716⟩

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