We review developments on generalized Fréchet functionals aiming at describing the possible influence of dependence on functionals of a statistical experiment, where the marginal distributions are fixed. The problem of mass transportation between two masses (distributions) can be seen as a particular case of this problem with two marginals and a linear functional induced by a distance. We also describe several results for the solution for nonlinear functionals in the context of the analysis of worst case risk distributions. We show that these problems can be reduced to a variational problem and the solution of a finite
class of (linear) mass transportation problems.
In the third part of the talk we review several recent methods to improve bounds for aggregated portfolios of risks by including additional to the marginal information some structural and partial dependence information. Several applications show that these improved risk bounds may lead to results acceptable in praxis.
Please attend this Dr. Rüschendorf's colloquium on Thursday, January 14th at 1 PM CST via this Zoom link, passcode 692674.