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Extremal negative dependence concepts
Giovanni Puccetti (University of Florence, Italy)
14:00-15:00, salle Extranef 125
While the concept of extremal positive dependence is agreed upon for random vectors of arbitrary dimension, various notions of extremal negative dependence arise when more than two random variables are involved. We will review popular existing concepts of extremal negative dependence given in the literature and introduce a novel notion, which in a general sense includes the existing ones as particular cases. Although much of the literature on dependence is actually focused on positive dependence, we will show that negative dependence plays an equally important role in the solution of many optimization problems. This talk is based on a joint work with Ruodu Wang, University of Waterloo.
| 6 mars 2015
The diameter of a random elliptical cloud
Philippe Soulier (Université Paris Ouest Nanterre, France)
14:00-15:00, salle Extranef 110
We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. d-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max-U-statistic, hence a maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributions. We obtain exhaustive results for the Euclidean diameter of a cloud of elliptical vectors whose Euclidean norm is in the domain of attraction for the maximum of the Gumbel distribution. We also obtain results in other norms for spherical vectors and we give several bi-dimensional generalizations. The main idea behind our results and their proofs is a specific property of random vectors whose norm is in the domain of attraction of the Gumbel distribution: the localization into subspaces of low dimension of vectors with a large norm. Joint work with Yann Demichel and Ana Karina Fermin.
|18 mars 2015
David Veredas (ECARES, Solvay Brussels School of Economics and Management, Université libre de Bruxelles, Belgium)
15:00-16:00, salle Extranef 125
Economic and financial crises are characterized by tail events. When they occur their effect is spread over the system creating tail correlations, which have linear and nonlinear origins. The former is due to the Pearson correlations while the latter is explained by the tail index. We introduce TailCoR, a new metric for tail correlations that has numerous advantages. It is simple to compute and distribution free, and it disentangles straightforwardly the linear and non-linear origins. When applied to a panel of eight major US banks, TailCoR increases during the financial crisis due to a surge of both linear and non-linear contributions. The end of 2012 also shows an increase of TailCoR, which is solely driven by the non-linearity, reflecting the risks of tail events and their contagion associated with the European sovereign debt crisis.
|24 avril 2015
Olaf Menkens (Dublin City University, Ireland)
14:00-15:00, salle Extranef 126
|22 mai 2015
Eckhard Platen (University of Technology, Sydney, Australia)
14:00-15:00, salle Extranef 109
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