Title: Extremes of extendible random vectors
Authors: Johanna Neslehova - McGill University (Canada) [presenting]
Klaus Herrmann - University of Waterloo (Canada)
Marius Hofert - University of Waterloo (Canada)
Abstract: Classical extreme value theory is concerned with the limiting behavior of maxima of independent and identically distributed random variables under appropriate location-scale transformations. When working with large portfolios, the assumption of independence may no longer be appropriate. We will explore the weak limits of maxima of identically distributed random variables which are neither independent nor form a locally dependent time series. A particularly tractable case is that of an extendible sequence of random variables whose dependence is Archimedean. As we will see, the possible limits are no longer extreme-value distributions, but an asymptotic theory for maxima can nonetheless be developed and is driven by the properties of the Archimedean generator. Extensions of these findings to other extendible sequences of random variables will also be discussed.