Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes
- Loisel, Stéphane Université de Lyon 1, Laboratoire SAF, Institut de Science Financière et d’Assurances, Lyon, France
- Mazza, Christian Department of Mathematics, University of Fribourg, Switzerland
- Rullière, Didier Université de Lyon 1, Laboratoire SAF, Institut de Science Financière et d’Assurances, Lyon, France
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22.08.2009
Published in:
- Insurance: Mathematics and Economics. - 2009, vol. 45, no. 3, p. 374-381
Finite-time ruin probability
Robustness
Solvency II
Reliable ruin probability
Asymptotic normality
Influence function
Estimation Risk Solvency Margin (ERSM)
Partly shifted risk process
English
In the classical risk model, we prove the weak convergence of a sequence of empirical finite-time ruin probabilities. In an earlier paper (see Loisel et al., (2008)), we proved an equivalent result in the special case where the initial reserve is zero, and checked that numerically the general case seems to be true. In this paper, we prove the general case (with a nonnegative initial reserve), which is important for applications to estimation risk. 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 and gives a useful tool to quantify estimation risk according to new regulations.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 17023
- DOI 10.1016/j.insmatheco.2009.08.003
- Persistent URL
- https://folia.unifr.ch/unifr/documents/301492
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