Computation of sharp bounds on the expected value of a supermodular function of risks with given marginals

We show that the rearrangement algorithm (RA) 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 to the analytical methods existing in the literature the algorithm is widely applicable, more easily obtained and gives insight into the dependence structures attaining the bounds.