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On the efficient simulation of the left-tail of the sum of correlated log-normal variates

On the efficient simulation of the left-tail of the sum of correlated log-normal variates AbstractThe sum of log-normal variates is encountered in many challenging applications such as performance analysis of wireless communication systems and financial engineering. Several approximation methods have been reported in the literature. However, these methods are not accurate in the tail regions. These regions are of primordial interest as small probability values have to be evaluated with high precision. Variance reduction techniques are known to yield accurate, yet efficient, estimates of small probability values. Most of the existing approaches have focused on estimating the right-tail of the sum of log-normal random variables (RVs). Here, we instead consider the left-tail of the sum of correlated log-normal variates with Gaussian copula, under a mild assumption on the covariance matrix. We propose an estimator combining an existing mean-shifting importance sampling approach with a control variate technique. This estimator has an asymptotically vanishing relative error, which represents a major finding in the context of the left-tail simulation of the sum of log-normal RVs. Finally, we perform simulations to evaluate the performances of the proposed estimator in comparison with existing ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monte Carlo Methods and Applications de Gruyter

On the efficient simulation of the left-tail of the sum of correlated log-normal variates

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1569-3961
eISSN
1569-3961
DOI
10.1515/mcma-2018-0009
Publisher site
See Article on Publisher Site

Abstract

AbstractThe sum of log-normal variates is encountered in many challenging applications such as performance analysis of wireless communication systems and financial engineering. Several approximation methods have been reported in the literature. However, these methods are not accurate in the tail regions. These regions are of primordial interest as small probability values have to be evaluated with high precision. Variance reduction techniques are known to yield accurate, yet efficient, estimates of small probability values. Most of the existing approaches have focused on estimating the right-tail of the sum of log-normal random variables (RVs). Here, we instead consider the left-tail of the sum of correlated log-normal variates with Gaussian copula, under a mild assumption on the covariance matrix. We propose an estimator combining an existing mean-shifting importance sampling approach with a control variate technique. This estimator has an asymptotically vanishing relative error, which represents a major finding in the context of the left-tail simulation of the sum of log-normal RVs. Finally, we perform simulations to evaluate the performances of the proposed estimator in comparison with existing ones.

Journal

Monte Carlo Methods and Applications – de Gruyter

Published: Jun 1, 2018

References

  • Efficient simulation of tail probabilities of sums of dependent random variables
  • On the distribution function and moments of power sums with lognormal component
  • Exponential family techniques for the lognormal left tail