Polyhedral Coherent Risk Measure and Distributionally Robust Portfolio Optimization

Polyhedral coherent risk measures and their worst-case constructions with respect to the ambiguity set are considered. For the case of the discrete distribution and polyhedral ambiguity set, calculating such risk measures reduces to linear programming problems. The distributionally robust portfolio optimization problems based on the reward-risk ratio using worst-case constructions with respect to the polyhedral ambiguity set for these risk measures and average return are analyzed. They are reduced to the appropriate linear programming problems.