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 -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}
}