High-dimensional dependence modeling using copulas

Copulas have been introduced more than half a century ago and represent a significant breakthrough in the study of dependencies between random variables, as they allow to do so free of any concern for the univariate margins, which, by definition, have nothing to do with the way the random variables interact with one another. However, while the framework for copulas is well established, the problem of finding actual copulas remains. The development of bivariate copulas (d=2) toke off during the last decades, but satisfying multidimensional copulas (d>2) are still lacking, with the possible exception of vine copulas. In this thesis, the development of multidimensional copulas is pushed further, in an effort to better understand multidimensional random phenoma. This includes new developments for a particular kind of graphs, called phylogenetic trees, research on nested Archimedean copulas, and the extension of factor copulas.