Distributionally robust return-risk optimization models and their applications. (English) Zbl 1442.91120

Summary: 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 random vector). It is difficult to solve them directly. Using the conic duality theory and the minimax theorem, the models 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 the models. Moreover, an application of the models 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.


91G70 Statistical methods; risk measures
90C22 Semidefinite programming
90C46 Optimality conditions and duality in mathematical programming
91G10 Portfolio theory


Full Text: DOI


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