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Efficient simulation of tail probabilities for sums of log-elliptical risks
- Source :
-
Journal of Computational & Applied Mathematics . Aug2013, Vol. 247, p53-67. 15p. - Publication Year :
- 2013
-
Abstract
- 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]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 247
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 85853775
- Full Text :
- https://doi.org/10.1016/j.cam.2012.11.025