Article: article from journal or magazin.
Efficient simulation of tail probabilities for sums of log-elliptical risks
Journal of Computational and Applied Mathematics
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 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.
Asmussen-Kroese estimator, Rojas-Nandayapa estimator, Log-elliptical distribution, Log-Gaussian distribution, Asymptotically vanishing relative error
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