Symmetric Adjustable Tail-Risk Measure for Distributionally Robust Optimization in Portfolio Allocation

In this study, we begin by extending the mathematical formulation of the expectile risk measure through a key modification: replacing the expectation in its defining equation with expected shortfall. This substitution leads to a revised risk measure that more precisely captures downside risk. To handle the uncertainty of the underlying distribution, we then adopt a distributionally robust optimization framework. Notably, this robust optimization problem can be reformulated as a linear programming problem, and by employing suitable approximation techniques, we derive an analytical solution. In numerical experiments, our portfolio problem exhibits superior performance when compared to several traditional and distributionally robust optimized portfolio problems.