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Efficient simulation of tail probabilities for sums of log-elliptical risks

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Publication date 2013
Author Kortschak Dominik, Hashorva Enkelejd,
Project Extremes of Gaussian Processes and Related Random Fields
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Original article (peer-reviewed)

Journal Journal of Computational and Applied Mathematics
Volume (Issue) 247(1)
Page(s) 53 - 67
Title of proceedings Journal of Computational and Applied Mathematics
DOI 10.1016/j.cam.2012.11.025

Abstract

In the framework of dependent risks it is a crucial task for risk management purposes to quantify the probability that the aggregated risk exceeds some large value u. Motivated by Asmussen et al. (2011) [1] in this paper we introduce a modified Asmussen-Kroese estimator for simulation of the rare event that the aggregated risk exceeds u. We show that in the framework of log-Gaussian risks our novel estimator has the best possible performance i.e., it has asymptotically vanishing relative error. For the more general class of log-elliptical risks with marginal distributions in the Gumbel max-domain of attraction we propose a modified Rojas-Nandayapa estimator of the rare events of interest, which for specific importance sampling densities has a good logarithmic performance. Our numerical results presented in this paper demonstrate the excellent performance of our novel Asmussen-Kroese algorithm. © 2013 Elsevier B.V. All rights reserved.
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