Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2005-006 (July 05, 2005)

Worst-case conditional Value-at-Risk with application to robust portfolio management
by Shu-Shang Zhu and Masao Fukushima

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This paper considers the worst-case CVaR in the case where only partial information on the underlying probability distribution is given. The minimization of worst-case CVaR under the mixture distribution uncertainty, componentwise bounded uncertainty and ellipsoidal uncertainty are investigated. The application of worst-case CVaR to robust portfolio optimization is proposed, and the corresponding problems are cast as linear programs and second-order cone programs which can be efficiently solved. Market data simulation and Monte Carlo simulation examples are presented to illustrate the methods. Our approaches can be applied in many situations, including those outside of financial risk management.