Optimization with Reference-Based Robust Preference Constraints

Abstract

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.