Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints

Yongchao Liu, Rudabeh Meskarian, Huifu Xu
2017 SIAM Journal on Optimization  
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
more » ... onstructed 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.
doi:10.1137/16m106114x fatcat:qoceq4qer5hthmliglcapxbdsm