Efficient simulation of tail probabilities for sums of log-elliptical risks
Probability
2014-05-06 v1 Applications
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.
Cite
@article{arxiv.1405.0607,
title = {Efficient simulation of tail probabilities for sums of log-elliptical risks},
author = {D. Kortschak and E. Hashorva},
journal= {arXiv preprint arXiv:1405.0607},
year = {2014}
}