Peaks-over-threshold stability of multivariate generalized Pareto distributions

Michael Falk and Armelle Guillou

Journal of Multivariate Analysis, 2008, vol. 99, issue 4, 715-734

Abstract: It is well-known that the univariate generalized Pareto distributions (GPD) are characterized by their peaks-over-threshold (POT) stability. We extend this result to multivariate GPDs. It is also shown that this POT stability is asymptotically shared by distributions which are in a certain neighborhood of a multivariate GPD. A multivariate extreme value distribution is a typical example. The usefulness of the results is demonstrated by various applications. We immediately obtain, for example, that the excess distribution of a linear portfolio with positive weights ai, i

Keywords: Peaks-over-threshold; stability; Multivariate; extreme; value; distribution; Multivariate; generalized; Pareto; distribution; Excess; distribution; Linear; portfolio; Expected; shortfall (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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