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
Published in:
- Insurance: Mathematics and Economics. - 2009, vol. 45, no. 3, p. 374-381
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
-
-
Classification
-
Mathematics
-
License
-
License undefined
-
Identifiers
-
-
Persistent URL
-
https://folia.unifr.ch/unifr/documents/301492
Statistics
Document views: 37
File downloads: