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...

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different...

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we...

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.

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...

We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an...