Actuarial Science Seminar: On a construction of multivariate distributions given some multidimensional marginals

We investigate the link between the joint law of a d-dimensional random vector and the law of some of its multivariate marginals. We introduce and focus on a class of distributions, that we call projective, for which we give detailed properties. This allows us to obtain necessary conditions for a given construction to be projective. We illustrate our results by proposing some theoretical projective distributions, as elliptical distributions or a new class of distribution having given bivariate margins. In the case where the data do not necessarily correspond to a projective distribution, we also explain how to build proper distributions while checking that the distance to the prescribed projections is small enough. Joint work with Nabil Kazi-Tani, preprint available at https://hal.archives-ouvertes.fr/hal-01575169v2