Statistical methodology of copulas with applications to economics.

In this research project I would like to focus on developing statistical methodology of copulas for applications in economics. Copulas are mathematical objects that are well suited to model and study interrelations between multidimensional observations of real life processes. In the recent years there has been a tremendous boost in demand for applications of copulas in various elds of science and engineering. Subsequently several scientic research groups all over the world established solid theoretical background of many copula properties that can be explored by practitioners. Similarly a signicant consideration was given to applicability and interpretability of the copula features and models and lead to a considerable number of simulation studies conducted by the research community. Despite the e ort of the scientic community the demand for copula understanding is still rising and new elds of possible applications emerge, in particular, in economics. Although copulas are widely involved in the eld of nance they are far less popularized in the insurance world, where, for example, they could enhance portfolio analysis for individual claims reserving. Moreover often economic processes can be represented as interactions between nodes in a graph or a network. The link between these structures and hierarchical copula representation leads to another unexplored area to investigate.