Stopping Times Occurring Simultaneously

Philip Protter and Alejandra Quintos

Papers from arXiv.org

Abstract: Stopping times are used in applications to model random arrivals. A standard assumption in many models is that they are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. We use a modified Cox construction along with the bivariate exponential introduced by Marshall and Olkin (1967) to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We show that our initial construction only allows for positive dependence between stopping times, but we also propose a joint distribution that allows for negative dependence while preserving the property of non-zero probability of equality. We indicate applications to modeling COVID-19 contagion (and epidemics in general), civil engineering, and to credit risk.

Date: 2021-11, Revised 2024-11
New Economics Papers: this item is included in nep-rmg
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Published in ESAIM: PS 28 (2024) 110-131

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2111.09458

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