Abstract:

This article studies the reward-risk optimization model under the uncertain distribution of random variables. In view of the three typical problems of traditional reward-risk and the background of uncertainty of distributions, a new model of distributionally robust reward-risk optimization is proposed under more general conditions. Based on moment ambiguity set and optimal duality theory, the complex new optimization model is simplified to a nonlinear optimization problem of conventional structure. The equivalence of efficient frontier of three types of distributionally robust reward-risk optimization models is proved theoretically. Numerical example verifies the effectiveness of the theoretical analysis.

Key words: reward-risk optimization problems, distributionally robust optimization, efficient frontier, robust counterpart