Characterizations of classes of risk measures by dispersive orders

In this paper, a class C1 of risk measures, which generalizes the class of risk measures for the right-tail deviation suggested by Wang [Wang, S., 1998. An actuarial index of the right-tail risk. North Amer. Actuarial J. 2, 88-101], is characterized in terms of dispersive order. If dispersive order does not hold, unanimous comparisons are still possible by restricting our attention to a subclass C2⊂C1 and then the criterion is the excess-wealth order. Sufficient conditions for stochastic equivalence of excess-wealth ordered random variables are derived in terms of some particular measures of C2.