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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 . 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 . 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. [Copyright &y& Elsevier]