We refine some criteria for the convex comparison of martingale densities suggested in Franke et al. (1999) and Bellini and Sgarra (2012). We give sufficient conditions for comparison based on the classical notion of comparative convexity. We apply these conditions to the case of minimal...

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...