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Res."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>This paper develops a unified algorithm to address the Conditional Value at Risk (CVaR) optimization problem characterized by two levels of expectations, where the inner-level expectation handles the repricing of the financial instruments and the outer-level expectation represents the risk measure. We propose an FA\u2013SAA algorithm that tackles the inner-level expectation through function approximation (FA) method and addresses the outer-level expectation by sample average approximation (SAA). A variety of machine learning methods can be incorporated into this algorithm and eventually the optimization problem is reformulated into a linear programming problem, whose optimal value and optimal solution converge to the actual ones. Besides, we demonstrate that the convergence rate of optimal value can achieve [Formula: see text]. The numerical results substantiate the efficacy of our proposed algorithm.<\/jats:p>","DOI":"10.1142\/s0217595925400020","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T09:36:16Z","timestamp":1738575376000},"source":"Crossref","is-referenced-by-count":1,"title":["The FA\u2013SAA Algorithm for CVaR Optimization"],"prefix":"10.1142","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8295-5189","authenticated-orcid":false,"given":"Nifei","family":"Lin","sequence":"first","affiliation":[{"name":"School of Management, Fudan University, Shanghai 200433, P. R. 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