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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.08983 |
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| _version_ | 1866913397992325120 |
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| author | Calzolari, Antonella Torti, Barbara |
| author_facet | Calzolari, Antonella Torti, Barbara |
| contents | We study the predictable representation property in the progressive enlargement F^τof a reference filtration F by a random time τ. Our approach is based on the decomposition of any random time into two parts, one overlapping F-stopping times (thin part) and the other one that avoids F-stopping times (thick part). We assume that the F-thin part of τis nontrivial and prove a martingale representation theorem on F^τ. We thus extend previous results dealing with F-avoiding random times. We collect some examples of application to the enlargement of the natural filtration of a Lévy process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thin-thick approach to martingale representations on progressively enlarged filtrations Calzolari, Antonella Torti, Barbara Probability We study the predictable representation property in the progressive enlargement F^τof a reference filtration F by a random time τ. Our approach is based on the decomposition of any random time into two parts, one overlapping F-stopping times (thin part) and the other one that avoids F-stopping times (thick part). We assume that the F-thin part of τis nontrivial and prove a martingale representation theorem on F^τ. We thus extend previous results dealing with F-avoiding random times. We collect some examples of application to the enlargement of the natural filtration of a Lévy process. |
| title | Thin-thick approach to martingale representations on progressively enlarged filtrations |
| topic | Probability |
| url | https://arxiv.org/abs/2406.08983 |