Tid: 29 oktober 2001 kl 1515-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Henrik Hult, Matematisk statistik, KTH
Titel: Multivariate extremes and dependence in elliptical distributions
In risk management log-returns are often assumed to have a multivariate normal distribution, but the multivariate normal distribution is unable to capture the dependence structure of the tails in most financial data sets. Therefore we need more sophisticated tools for measuring and analysing dependence of tails. In this talk we will focus on dependence measures for elliptical distributions. Elliptical distributions are easy to understand and share many of the tractable properties of the multivariate normal distribution, but they also enable modelling multivariate extremes and other forms of non-normal dependencies. Furthermore, they allow for explicit computation of interesting quantities such as tail dependence coefficients and the spectral measure (which will be introduced in the talk). As an example we will use the spectral measure with respect to the max norm to answer questions like: What is the dependence structure between the components in a d-dimensional random vector given that at least one component is extreme? We will also discuss the relation between dependence measures such as correlation, Kendall's tau, and Spearman's rho in the case of elliptical distributions.
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