TY - JOUR

T1 - On the efficient simulation of the left-tail of the sum of correlated log-normal variates

AU - Alouini, Mohamed-Slim

AU - Rached, Nadhir B.

AU - Kammoun, Abla

AU - Tempone, Raul

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2018/4/4

Y1 - 2018/4/4

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/626530

UR - http://arxiv.org/abs/1705.07635v2

UR - http://www.scopus.com/inward/record.url?scp=85045838184&partnerID=8YFLogxK

U2 - 10.1515/mcma-2018-0009

DO - 10.1515/mcma-2018-0009

M3 - Article

SN - 0929-9629

VL - 24

SP - 101

EP - 115

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

IS - 2

ER -