2017/05/22 by Mohamed‐Slim Alouini, Alouini, Mohamed-Slim, Nadhir Ben Rached +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1705.07635
openalex publication_date 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sum of Log-normal variates is encountered in many challenging\napplications such as in performance analysis of wireless communication systems\nand in financial engineering. Several approximation methods have been developed\nin the literature, the accuracy of which is not ensured in the tail regions.\nThese regions are of primordial interest wherein small probability values have\nto be evaluated with high precision. Variance reduction techniques are known to\nyield accurate, yet efficient, estimates of small probability values. Most of\nthe existing approaches, however, have considered the problem of estimating the\nright-tail of the sum of Log-normal random variables (RVS). In the present\nwork, we consider instead the estimation of the left-tail of the sum of\ncorrelated Log-normal variates with Gaussian copula under a mild assumption on\nthe covariance matrix. We propose an estimator combining an existing\nmean-shifting importance sampling approach with a control variate technique.\nThe main result is that the proposed estimator has an asymptotically vanishing\nrelative error which represents a major finding in the context of the left-tail\nsimulation of the sum of Log-normal RVs. Finally, we assess by various\nsimulation results the performances of the proposed estimator compared to\nexisting estimators.\n