A Semi-Infinite Programming Approach for Distributionally Robust Reward-Risk Ratio Optimization with Matrix Moments Constraints1

Reward-risk ratio optimization is an important mathematical approach in finance [54]. In this paper, we revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken against the risk arising from ambiguity of the true distribution. We propose a distributionally robust reward-risk ratio optimization model where the ambiguity set is constructed through simple inequality moment constraints and develop efficient numerical methods for solving the problem: first, we transform the robust optimization problem into a nonlinear semi-infinite programming problem through Lagrange dualization and then use the well known entropic risk measure to construct an approximation of the semi-infinite constraints, we solve the latter by an implicit Dinkelbach method (IDM). Finally, we apply the proposed robust model and numerical scheme to a portfolio optimization problem and report some preliminary numerical test results.