Convex comparison of minimal divergence martingale measures in discrete time models

We refine some criteria for the convex comparison of martingale densities suggested in Franke et al. [11] and Bellini and Sgarra [4]. We give sufficient conditions for comparison based on the classical notion of comparative convexity. We apply these conditions to the case of minimal f-divergence martingale measures, establishing an ordering result in the case of power divergences. We discuss the extension of the comparison to a multiperiod setting and provide several numerical examples.