Stopping times occurring simultaneously.

Protter, Philip; Quintos, Alejandra

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.

CREDIT risk; STOCHASTIC processes; CIVIL engineers; TIME management; CIVIL engineering

ESAIM: Probability & Statistics, 2024, Vol 28, p110

1292-8100

Academic Journal

10.1051/ps/2024001