English

Archimedean Survival Processes

General Finance 2012-09-19 v4 Probability

Abstract

Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. A. J. McNeil and J. Ne\v{s}lehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate 1\ell_1-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 multivariate gamma process, 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.

Cite

@article{arxiv.1106.2342,
  title  = {Archimedean Survival Processes},
  author = {Edward Hoyle and Levent Ali Menguturk},
  journal= {arXiv preprint arXiv:1106.2342},
  year   = {2012}
}
R2 v1 2026-06-21T18:21:11.312Z