Conditional value-at-risk for general loss distributions |
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| Affiliation: | 1. Department of Mathematics, University of Washington, P.O. Box 354350, Seattle, WA 98195-4350, USA;2. Risk Management and Financial Engineering Lab, Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, Gainesville, FL 32611-6595, USA;1. Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China;2. State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China;1. Dept. of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816, USA;2. Argonne National Laboratory, Argonne, IL 60439, USA;1. School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, 310027, China;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;1. Department of Industrial Engineering, Dokuz Eylul University, Turkey 35397, Izmir, Turkey;2. Department of Industrial Engineering, Izmir Bakircay University, 35665 Izmir, Turkey |
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| Abstract: | Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR and moreover it is coherent. It provides optimization short-cuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking. |
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