Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas
Abstract
This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the possibility to sample final multivariate survival in a long time-interval as a sequence of iterations of local multivariate survivals along a partition of the total time interval. We find that this is possible under a form of multivariate lack of memory that is linked to a property of the survival times copula. This property defines a "self-chaining-copula", and we show that this coincides with the extreme value copulas characterization. The self-chaining condition is satisfied by the Gumbel-Hougaard copula, a full characterization of self chaining copulas in the Archimedean family, and by the Marshall-Olkin copula. The result has important practical implications for consistent single-step and multi-step simulation of multivariate arrival times in a way that does not destroy dependency through iterations, as happens when inconsistently iterating a Gaussian copula.
Cite
@article{arxiv.1204.2090,
title = {Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas},
author = {Damiano Brigo and Kyriakos Chourdakis},
journal= {arXiv preprint arXiv:1204.2090},
year = {2012}
}