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.

As the dynamic mean-variance portfolio selection formulation does not satisfy the principle of optimality of dynamic programming, phenomena of time inconsistency occur, i.e., investors may have incentives to deviate from the precommitted optimal mean-variance portfolio policy during the investment process under certain circumstances. By introducing the concept of time inconsistency in efficiency and defining the induced trade-off, we further demonstrate in this paper that investors behave irrationally under the precommitted optimal mean-variance portfolio policy when their wealth is above certain threshold during the investment process. By relaxing the selffinancing restriction to allow withdrawal of money out of the market, we develop a revised mean-variance policy which dominates the precommitted optimal mean-variance portfolio policy in the sense that, while the two achieve the same mean-variance pair of the terminal wealth, the revised policy enables the investor to receive a free cash flow stream (FCFS) during the investment process. The analytical expressions of the probability of receiving FCFS and the expected value of FCFS are derived.

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