In the statistical and actuarial literature several generalizations of quantiles have been considered, by means of the minimization of a suitable asymmetric loss function. All these generalized quantiles share the important property of elicitability, that is recently receiving a lot of attention...

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...

Abstract We deal with the problem of the practical use of Haezendonck risk measures (see Haezendonck and Goovaerts [8], Goovaerts et al. [7], Bellini and Rosazza Gianin [4]) in portfolio optimization. We first analyze the properties of the natural estimators of Haezendonck risk measures by means...

In this paper we provide an axiomatic foundation to Orlicz risk measures in terms of properties of their acceptance sets, by exploiting their natural correspondence with shortfall risk measures, thus paralleling the characterization in Weber (2006). From a financial point of view, Orlicz risk...