Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints

Reward-risk ratio optimization is an important mathematical approach in finance. 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 to mitigate the risk arising from ambiguity of the true distribution. We consider a distributionally robust reward-risk ratio optimization model varied from ex ante Sharpe ratio where the ambiguity set is constructed through prior moment information and the return function is not necessarily linear. We transform the robust optimization problem into a nonlinear semi-infinite programming problem through standard 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. The proposed robust formulation and numerical schemes can be easily applied to stochastic fractional programming problems.