Convergence and asymptotic variance of bootstrapped finitetime 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. 374381
English
In the classical risk model, we prove the weak convergence of a sequence of empirical finitetime 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. Socalled 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

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Mathematics

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https://folia.unifr.ch/unifr/documents/301492
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