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...

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...