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# Archimedean Survival Processes

## Author

Listed:
• Edward Hoyle
• Levent Ali Menguturk

## 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 $\ell_1$-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.

## Suggested Citation

• Edward Hoyle & Levent Ali Menguturk, 2011. "Archimedean Survival Processes," Papers 1106.2342, arXiv.org, revised Sep 2012.
• Handle: RePEc:arx:papers:1106.2342
as

File URL: http://arxiv.org/pdf/1106.2342

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