Abstract In this paper, we survey, extend and improve several bounds for the distribution function and the tail probabilities of portfolios, where the dependence structure within the portfolio is completely unknown or only partially known. We present various methods for obtaining bounds based on...

We introduce the concepts of ϕ-complete mixability and ϕ-joint mixability and we investigate some necessary and sufficient conditions to the ϕ-mixability of a set of distribution functions for some supermodular functions ϕ. We give examples and numerical verifications which confirm our findings.

We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence...

This paper presents an investigation of the transmitted power in a wireless power transfer system that employs a metamaterial. Metamaterials are a good means to transfer power wirelessly, as they are composed of multiple inductively-coupled resonators. The system can be designed and matched...

Using a connection between the rearrangement algorithm introduced in Puccetti and Rüschendorf (2012) and convex order, we show how to compute the best-possible expected shortfall for the sum of d random variables having fixed marginal distributions.

We give a new sufficient condition for a continuous distribution to be completely mixable, and we use this condition to show that the worst-possible value-at-risk for the sum of d inhomogeneous risks is equivalent to the worst-possible expected shortfall under the same marginal assumptions, in...

In this paper we consider several multivariate extensions of comonotonicity. We show that naive extensions do not enjoy some of the main properties of the univariate concept. In order to have these properties, more structures are needed than in the univariate case.

In this paper, a theoretical and experimental analysis of wireless power transfer through a coplanar resonator array is presented. In particular, six identical spiral resonators are used to form an array and transfer power between an emitter and a receiver. All the spiral resonators resonate at...

The Wasserstein barycenter is an important notion in the analysis of high dimensional data with a broad range of applications in applied probability, economics, statistics, and in particular to clustering and image processing. We state a general version of the equivalence of the Wasserstein...