Optimization with Reference-Based Robust Preference Constraints
提出一种基于参考的几乎随机占优（RSD）的稳健偏好关系，用于优化模型，解决决策者风险态度刻画中的模糊性和随机占优的过度保守问题，并通过投资组合优化验证效果。
We propose an optimization model using a novel robust preference relationship---reference-based almost stochastic dominance (RSD). The concept of RSD addresses the two problems in utility-based decision making: (i) ambiguity and inaccuracy in characterizing the decision maker's individual risk attitude, and (ii) overconservativeness of stochastic dominance representing general properties of risk aversion. The RSD rule reveals the maximum dominance level quantifying the robustness of the decision maker's preference between alternative choices. We first develop an approximation model using Bernstein polynomials, show the asymptotic convergence of its optimal value and set of optimal solutions to their true counterparts as the degree of Bernstein polynomials increases, and analyze the convergence rate of its feasible region. We next develop a cut-generation algorithm to solve the approximation model. Finally, we further adapt this cut-generation algorithm to seek a valid option most robustly preferable to a random benchmark. The effectiveness and computational complexity of the model have been illustrated using a portfolio optimization problem.