  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.
