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 investigate the set of centers of completely and jointly mixable distributions. In addition to several results, we show that, for each n ≥ 2, there exist n standard Cauchy random variables adding up to a constant C if and only if |C| ≤ n*log(n − 1)/π

We introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson's correlation in arbitrary dimensions. The new measure and its bounds are derived from a mass transportation approach in which the expected inner...

We study a synchronization problem with multiple instances. First, we show that the problem we consider can be formulated as the problem of finding an intra-column rearrangement for multiple matrices (which reflect problem instances) such that the row sums across the various matrices show...

We introduce a new algorithm, called the swapping algorithm, to approximate numerically the minimal and maximal expected inner product of two random vectors with given marginal distributions. As a direct application, the algorithm computes an approximation of the L2-Wasserstein distance between...

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...

Most banks use the top-down approach to aggregate their risk types when computing total economic capital. Following this approach, marginal distributions for each risk type are first independently estimated and then merged into a joint model using a copula function. Due to lack of reliable data,...