 Confidence Levels for CVaR Risk Measures and Minimax Limits*Edward Anderson, Huifu Xu and Dali Zhang No 2014_01, Working Papers from University of Sydney Business School, Discipline of Business Analytics Abstract: Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and it's impact on optimal decision making when we wish to minimize the respective risk measures. We also investigate the difference between the optimal solutions to the two optimization problems with identical objective function but under constraints on the two risk measures. We discuss the benefits of a sample average approximation scheme for the CVaR constraints and investigate the convergence of the optimal solution obtained from this scheme as the sample size increases. We use some portfolio optimization problems to investigate teh performance of the CVaR approximation approach. Our numerical results demonstrate how reducing the confidence level can lead to a better overall performanc e. Keywords: CVaR approximation; robust optimization; minimax; semi-infinate programming; distributional robust optimization; sample average approximation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:syb:wpbsba:2123/9943 Access Statistics for this paper More papers in Working Papers from University of Sydney Business School, Discipline of Business Analytics Contact information at EDIRC. |
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