On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

German Bernhart 1 , Jan-Frederik Mai 2 , and Matthias Scherer 1
  • 1 Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • 2 XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany

Abstract

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

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