In 1959 Abe Sklar published the first version of the famous copula function theorem. Sixty years later, this series of lectures is aimed at introducing the concept and discussing the frontier issues of the application of this tool to several fields, with a particular bias of the author towards finance and economics, but will to hear about other fields of applications. The main goal will be to convey and receive ideas for original research on the subject.

Copula functions: back to the future

1. Sklar, Gauss and “the formula that killed Wall Street
2. Elliptical, Archimedean, what else?
3. Basic applications

Copula function estimation

1. The likelihood approach
2. The MM and SMM approach
3. Exchangeability, singularity and other issues

Copula functions go dynamic

1. Sklar meets Markov: the DNO approach
2. Convolution copulas

Copula functions and the singularity issue

1. What is the probability that two banks default at the same time?
2. Copulas with singular components: MO and GMO copulas
3. Systemic risk application

Dependence in large data sets

1. Gaussian copula applications for large graph models
2. Large dynamic models with applications