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Archimedean survival processes

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Volume
115
Identifiers
DOI: 10.1016/j.jmva.2012.09.008
Keywords
  • Archimedean Copula
  • Gamma Process
  • Gamma Bridge
  • Multivariate Liouville Distribution

Abstract

Abstract Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. McNeil and Nešlehová (2009) [12] showed that the class of Archimedean copulas coincides with the class of positive multivariate ℓ1-norm symmetric distributions. Building upon their results, we introduce a class of multivariate Markov processes that we call ‘Archimedean survival processes’ (ASPs). An ASP is defined over a finite time interval, is equivalent in law to a vector of independent gamma processes, and its terminal value has an Archimedean survival copula. There exists a bijection from the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation.

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