We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating...

We define a new family of central regions with respect to a probability measure. They are induced by a set or a family of sets of functions and we name them integral trimmed regions. The halfspace trimming and the zonoid trimming are particular cases of integral trimmed regions. We focus our...

Consider any kind of parameter for a probability distribution and a fixed distribution. We study the subsets of the parameter space constituted by all the parameters of the probabilities in the α-trimming of the fixed distribution. These sets will be referred to as parameter trimmed regions....

It is known that each symmetric stable distribution in is related to a norm on that makes embeddable in Lp([0,1]). In the case of a multivariate Cauchy distribution the unit ball in this norm is the polar set to a convex set in called a zonoid. This work interprets symmetric stable laws using...

The quantisation problem for probability measures aims to represent a measure using a discrete measure supported by a finite set . We consider a similar problem where is a realisation of a finite Poisson point process, the objective function is given by the expected Lp-error, and the constraints...

We define a new stochastic order for random vectors in terms of the inclusion relation for the Aumann expectation of certain random sets. We derive some properties of this order, relate it with other well-known multivariate stochastic convex orders, give a geometrical interpretation in terms of...

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations...