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

Alouini Mohamed-Slim (), Ben Rached Nadhir (), Kammoun Abla () and Tempone Raul ()
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Alouini Mohamed-Slim: Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal23955, Saudi Arabia
Ben Rached Nadhir: Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal23955, Saudi Arabia
Kammoun Abla: Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal23955, Saudi Arabia
Tempone Raul: Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal23955, Saudi Arabia

Monte Carlo Methods and Applications, 2018, vol. 24, issue 2, 101-115

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.

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 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/mcma-2018-0009

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