Several statistical functionals such as quantiles and expectiles arise naturally as the minimizers of the expected value of a scoring function, a property that is called elicitability (see Gneiting, 2011 and the references therein). The existence of such scoring functions gives a natural way to...

A statistical functional is elicitable if it can be defined as the minimizer of a suitable expected scoring function (see Gneiting (2011), Ziegel (2013) and the references therein). With financial applications in view, we suggest a slightly more restrictive definition than Gneiting (2011), and...

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...