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...

Based on a novel extension of classical Hoeffding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with fixed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a...

The quantile formulation for optimal portfolio selection problems under increasing law-invariant objectives allows to reduce any such problem to an optimization problem on real functions under monotonicity conditions. We solve two basic types of these optimization problems, which makes it...

We show that the rearrangement algorithm introduced in Puccetti and Rüschendorf (2012) to compute distributional bounds can be used also to compute sharp lower and upper bounds on the expected value of a supermodular function of d random variables having fixed marginal distributions. Compared...

We study the impact of dependence uncertainty on E(X_1X_2 · · · X_d) when X_i ∼ F_i for all i. Under some conditions on the Fi, explicit sharp bounds are obtained and a numerical method is provided to approximate them for arbitrary choices of the F_i. The results are applied to assess the...

The problem of the fair allocation of indivisible items is a relevant and challenging economic problem with several applications. For small dimensional frameworks, the problem can be solved exactly by full enumeration of all the possible allocations of the items. For higher dimensional...