{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T21:10:20Z","timestamp":1680383420806},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>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.<\/jats:p>","DOI":"10.1515\/mcma-2018-0009","type":"journal-article","created":{"date-parts":[[2018,4,4]],"date-time":"2018-04-04T17:01:41Z","timestamp":1522861301000},"page":"101-115","source":"Crossref","is-referenced-by-count":8,"title":["On the efficient simulation of the left-tail of the sum of correlated log-normal variates"],"prefix":"10.1515","volume":"24","author":[{"given":"Mohamed-Slim","family":"Alouini","sequence":"first","affiliation":[{"name":"Computer, Electrical and Mathematical Sciences and Engineering , King Abdullah University of Science and Technology (KAUST) , Thuwal 23955 , Saudi Arabia"}]},{"given":"Nadhir","family":"Ben Rached","sequence":"additional","affiliation":[{"name":"Computer, Electrical and Mathematical Sciences and Engineering , King Abdullah University of Science and Technology (KAUST) , Thuwal 23955 , Saudi Arabia"}]},{"given":"Abla","family":"Kammoun","sequence":"additional","affiliation":[{"name":"Computer, Electrical and Mathematical Sciences and Engineering , King Abdullah University of Science and Technology (KAUST) , Thuwal 23955 , Saudi Arabia"}]},{"given":"Raul","family":"Tempone","sequence":"additional","affiliation":[{"name":"Computer, Electrical and Mathematical Sciences and Engineering , King Abdullah University of Science and Technology (KAUST) , Thuwal 23955 , Saudi Arabia"}]}],"member":"374","published-online":{"date-parts":[[2018,3,30]]},"reference":[{"key":"2023040101343508972_j_mcma-2018-0009_ref_001_w2aab3b7b3b1b6b1ab1b6b1Aa","doi-asserted-by":"crossref","unstructured":"S.  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Probab. 18 (2014), no. 2, 441\u2013458.","DOI":"10.1007\/s11009-014-9430-7"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_004_w2aab3b7b3b1b6b1ab1b6b4Aa","doi-asserted-by":"crossref","unstructured":"S.  Asmussen, J. L.  Jensen and L.  Rojas-Nandayapa,\nExponential family techniques for the lognormal left tail,\nScand. J. Stat. 43 (2016), 774\u2013787.\n10.1111\/sjos.12203","DOI":"10.1111\/sjos.12203"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_005_w2aab3b7b3b1b6b1ab1b6b5Aa","doi-asserted-by":"crossref","unstructured":"S.  Asmussen and D. P.  Kroese,\nImproved algorithms for rare event simulation with heavy tails,\nAdv. in Appl. Probab. 38 (2006), no. 2, 545\u2013558.\n10.1017\/S0001867800001099","DOI":"10.1239\/aap\/1151337084"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_006_w2aab3b7b3b1b6b1ab1b6b6Aa","doi-asserted-by":"crossref","unstructured":"S.  Asmussen and L.  Rojas-Nandayapa,\nAsymptotics of sums of lognormal random variables with Gaussian copula,\nStatist. Probab. Lett. 78 (2008), 2709\u20132714.\n10.1016\/j.spl.2008.03.035","DOI":"10.1016\/j.spl.2008.03.035"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_007_w2aab3b7b3b1b6b1ab1b6b7Aa","doi-asserted-by":"crossref","unstructured":"N. C.  Beaulieu and Q.  Xie,\nAn optimal lognormal approximation to lognormal sum distributions,\nIEEE Trans. Vehicular Technol. 53 (2004), 479\u2013489.\n10.1109\/TVT.2004.823494","DOI":"10.1109\/TVT.2004.823494"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_008_w2aab3b7b3b1b6b1ab1b6b8Aa","doi-asserted-by":"crossref","unstructured":"N.  Ben Rached, F.  Benkhelifa, A.  Kammoun, M.-S.  Alouini and R.  Tempone,\nOn the generalization of the hazard rate twisting-based simulation approach,\nStat. Comput. 28 (2016), no. 1, 61\u201375.","DOI":"10.1007\/s11222-016-9716-4"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_009_w2aab3b7b3b1b6b1ab1b6b9Aa","doi-asserted-by":"crossref","unstructured":"N.  Ben Rached, A.  Kammoun, M.-S.  Alouini and R.  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Commun. 57 (2009), 388\u2013403.\n10.1109\/TCOMM.2009.02.0700402","DOI":"10.1109\/TCOMM.2009.02.0700402"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_012_w2aab3b7b3b1b6b1ab1b6c12Aa","doi-asserted-by":"crossref","unstructured":"M.  Di Renzo, F.  Graziosi and F.  Santucci,\nFurther results on the approximation of log-normal power sum via Pearson type IV distribution: A general formula for log-moments computation,\nIEEE Trans. Commun. 57 (2009), 893\u2013898.\n10.1109\/TCOMM.2009.04.070133","DOI":"10.1109\/TCOMM.2009.04.070133"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_013_w2aab3b7b3b1b6b1ab1b6c13Aa","doi-asserted-by":"crossref","unstructured":"D.  Dufresne,\nThe log-normal approximation in financial and other computations,\nAdv. in Appl. Probab. 36 (2004), 747\u2013773.\n10.1239\/aap\/1093962232","DOI":"10.1017\/S0001867800013094"},{"key":"2023040101343508972_j_mcma-2018-0009_ref_014_w2aab3b7b3b1b6b1ab1b6c14Aa","doi-asserted-by":"crossref","unstructured":"L.  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