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arXiv · 1405.0607

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

D. Kortschak·E. Hashorva
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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) 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. 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. Numerical results demonstrate the excellent performance of our novel Asmussen-Kroese algorithm.

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D. Kortschak, E. Hashorva. 2014-05-03. Efficient simulation of tail probabilities for sums of log-elliptical risks. https://doi.org/10.1016/j.cam.2012.11.025

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