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.