2012/04/10 by Damiano Brigo, Brigo, Damiano, Kyriakos Chourdakis +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E07 #62H05 #62H20 #62H99 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Forecasting Techniques and Applications #Market Dynamics and Volatility #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60E07 #msc:62H05 #msc:62H20 #msc:62H99 #q-fin.PR #stat.TH
paper · pdf · doi:10.48550/arxiv.1204.2090
openalex publication_date 2012/04/10 · arxiv created 2012/04/28 · arxiv updated 2012/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.