Abstract
This article examines the strong consistency of the conditional value-at-risk (CVaR) estimate for asymptotic negatively associated (ANA or ρ−\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\rho ^{-}$\\end{document}, for short) random samples under mild conditions. It is demonstrated that the optimal rate can achieve nearly O(n−1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$O (n^{-1/2})$\\end{document} under certain appropriate conditions. Furthermore, we present numerical simulations and a real data example to corroborate our theoretical results based on finite samples.
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