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This rare-event setting renders the naive Monte Carlo method inefficient and requires the use of variance reduction techniques. To address this issue, we develop a novel and strongly efficient method for the computation of the said expectation in a general rare-event setting by exploiting the geometry of the target polyhedron and concentrating the sampling density almost within the polyhedron. The proposed method significantly outperforms the existing approaches in various numerical experiments in terms of accuracy and computational costs.<\/jats:p>\n                  <jats:p>Funding: This research was supported by the Early Career Scheme from the Research Grants Council of Hong Kong, University Grants Committee [Grant CUHK 24210420] and the Chinese University of Hong Kong (CUHK) Direct Grant for Research [Grant 4055206].<\/jats:p>","DOI":"10.1287\/moor.2023.0145","type":"journal-article","created":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T10:44:14Z","timestamp":1747737854000},"page":"1312-1349","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Simulation of Polyhedral Expectations with Applications to Finance"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0304-0636","authenticated-orcid":false,"given":"Dohyun","family":"Ahn","sequence":"first","affiliation":[{"name":"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0685-3253","authenticated-orcid":false,"given":"Lewen","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1145\/3167969"},{"key":"B2","doi-asserted-by":"crossref","unstructured":"Ahn D, Zheng L (2021) Efficient simulation for linear programming under uncertainty.\n                      WSC \u201821 Proc. 2021 Winter Simulation Conf.\n                      (IEEE Press, Piscataway, NJ), 1\u201320.","DOI":"10.1109\/WSC52266.2021.9715308"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1017\/S1748499517000252"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-69033-9"},{"key":"B5","doi-asserted-by":"crossref","unstructured":"Bai Y, Lam H, Engelke S (2022a) Rare-event simulation without variance reduction: An extreme value theory approach. 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