Date: 2016-02-26

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, we will consider a portfolio of dependent risks represented by a vector of dependent random variables whose joint cumulative distribution function (CDF) is defined with an Archimedean copula. Archimedean copulas are very popular and their extensions, nested Archimedean copulas, are well suited for vectors of random vectors in high dimension. I will describe a simple approach which makes it possible to compute the CDF of the sum or a variety of other functions of those random variables. In particular, I will derive the CDF and the TVaR of the sum of those risks using the Frank copula, the Shifted Negative Binomial copula, and the Ali-Mikhail-Haq (AMH) copula. The computation of the contribution of each risk under the TVaR-based allocation rule will also be illustrated. Finally, the links between the Clayton copula, the Shifted Negative Binomial copula, and the AMH copula will be discussed.

Speaker

Etienne Marceau is a professor in the School of Actuarial Science at Université Laval, Québec City. His research interests include actuarial mathematics, risk theory, and dependence modeling. He is the author of numerous research articles and of the book « Modélisation et évaluation des risques en actuariat » (Springer, 2013).