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...

Optimal transportation w.r.t. the Kantorovich metric l1 (resp. the Wasser- stein metric W1) between two absolutely continuous measures is known since the basic papers of Kantorovich and Rubinstein (1957) and Sudakov (1979) to occur on rays induced by a decomposition of the basic space, which is...