Worst-case Omega ratio under distribution uncertainty with its application in robust portfolio selection

Omega ratio, a risk-return performance measure, is defined as the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. Motivated by finding a solution protected against sampling errors, in this paper, we focus on the worst-case Omega ratio under distributional uncertainty and its application to robust portfolio selection. The main idea is to deal with optimization problems with all uncertain parameters within an uncertainty set. The uncertainty set of the distribution of returns given characteristic information, including the first two orders of moments and the Wasserstein distance, can handle data problems with uncertainty while making the calculation feasible.