also called a capacity, the present paper gives a generalization to the case of a capacity of the classical notion of … quantile function with respect to the given capacity. Characterizations, involving Choquet integrals with respect to a … distorted capacity, are established for the classes of monetary risk measures (defined on the space of bounded real …

capacity. We give different characterizations of this relation establishing a link to the notions of distribution function and … quantile function with respect to the given capacity. The Choquet integral is extensively used as a tool. In the second part of … increasing convex stochastic dominance relation with respect to a capacity. The problem is solved by using, among other tools, a …