Distributionally Robust Return-Risk Optimization Models and Their Applications

Based on the risk control of conditional value-at-risk, distributionally robust return- risk optimization models with box constraints of random vector are proposed. They describe uncertainty in both the distribution form and moments (mean and covariance matrix of randomvector). It is difficult to solve them directly. Using the conic duality theory and the minimax theorem, themodels are reformulated as semidefinite programming problems, which can be solved by interior point algorithms in polynomial time. An important theoretical basis is therefore provided for applications of themodels. Moreover, an application of themodels to a practical example of portfolio selection is considered, and the example is evaluated using a historical data set of four stocks. Numerical results show that proposed methods are robust and the investment strategy is safe.