Alouini, M-S, Ben Rached, N, Kammoun, A et al. (1 more author) (2018) On the efficient simulation of the left-tail of the sum of correlated log-normal variates. Monte Carlo Methods and Applications, 24 (2). pp. 101-115. ISSN 0929-9629
Abstract
The 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article published in Monte Carlo Methods and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Sum of correlated log-normal; small probability values; variance reduction techniques; left-tail of the sum of correlated log-normal variates; importance sampling; control variate; asymptotically vanishing relative error |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 May 2023 12:50 |
Last Modified: | 22 May 2023 12:50 |
Published Version: | http://dx.doi.org/10.1515/mcma-2018-0009 |
Status: | Published |
Publisher: | De Gruyter |
Identification Number: | 10.1515/mcma-2018-0009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195467 |