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Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management

Department of Management Science, School of Management, Fudan University, Shanghai 200433, China
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
sszhu{at}fudan.edu.cn
fuku{at}i.kyoto-u.ac.jp

This paper considers the worst-case Conditional Value-at-Risk (CVaR) in the situation where only partial information on the underlying probability distribution is available. The minimization of the worst-case CVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. The application of the worst-case CVaR to robust portfolio optimization is proposed, and the corresponding problems are cast as linear programs and second-order cone programs that can be solved efficiently. Market data simulation and Monte Carlo simulation examples are presented to illustrate the proposed approach.

Subject classifications: conditional value-at-risk; portfolio management.
History: Received July 2005; revision received October 2008; accepted November 2008.