Stopping Times Occurring Simultaneously
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910705416929280 |
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| author | Protter, Philip Quintos, Alejandra |
| author_facet | Protter, Philip Quintos, Alejandra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09458 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stopping Times Occurring Simultaneously Protter, Philip Quintos, Alejandra Probability Mathematical Finance 60G40, 60G55, 91G40 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. |
| title | Stopping Times Occurring Simultaneously |
| topic | Probability Mathematical Finance 60G40, 60G55, 91G40 |
| url | https://arxiv.org/abs/2111.09458 |