Omega ratios have been introduced in Keating and Shadwick (2002) as a performance measure to compare the performance of different investment opportunities. It does not have some of the drawbacks of the famous Sharpe ratio. In particular, it is consistent with first order stochastic dominance....

We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the...

In this paper we introduce the expectile order, defined by X \leq_e Y if e_\alpha(X) \leq e_\alpha(Y) for each \alpha \in (0,1), where e_\alpha denotes the \alpha-expectile. We show that the expectile order is equivalent to the pointwise ordering of the Omega ratios, and we derive several...