Non-arbitrage under a class of honest times
This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc in which the authors studied similar topics for the...
| Main Authors: | , , , |
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| Format: | Journal article |
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2017
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| _version_ | 1826267099437203456 |
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| author | Choulli, T Aksamit, A Deng, J Jeanblanc, M |
| author_facet | Choulli, T Aksamit, A Deng, J Jeanblanc, M |
| author_sort | Choulli, T |
| collection | OXFORD |
| description | This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc in which the authors studied similar topics for the case of stopping at the random time instead, while herein we are concerned with the part after the occurrence of the random time. Given that all the literature -up to our knowledge- proves that the NUPBR notion is always violated after honest times that avoid stopping times in a continuous filtration, herein we propose a new class of honest times for which the NUPBR notion can be preserved for some models. For this family of honest times, we elaborate two principal results. The first main result characterizes the pairs of initial market and honest time for which the resulting model preserves the NUPBR property, while the second main result characterizes the honest times that preserve the NUPBR property for any quasi-left continuous model. Furthermore, we construct explicitly "the-after-tau" local martingale deflators for a large class of initial models (i.e. models in the small filtration) that are already risk-neutralized. |
| first_indexed | 2024-03-06T20:49:00Z |
| format | Journal article |
| id | oxford-uuid:36eec47a-4f3a-4340-b56d-a9ab81dd9bc1 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:49:00Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oxford-uuid:36eec47a-4f3a-4340-b56d-a9ab81dd9bc12022-03-26T13:41:01ZNon-arbitrage under a class of honest timesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:36eec47a-4f3a-4340-b56d-a9ab81dd9bc1Symplectic Elements at Oxford2017Choulli, TAksamit, ADeng, JJeanblanc, MThis paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc in which the authors studied similar topics for the case of stopping at the random time instead, while herein we are concerned with the part after the occurrence of the random time. Given that all the literature -up to our knowledge- proves that the NUPBR notion is always violated after honest times that avoid stopping times in a continuous filtration, herein we propose a new class of honest times for which the NUPBR notion can be preserved for some models. For this family of honest times, we elaborate two principal results. The first main result characterizes the pairs of initial market and honest time for which the resulting model preserves the NUPBR property, while the second main result characterizes the honest times that preserve the NUPBR property for any quasi-left continuous model. Furthermore, we construct explicitly "the-after-tau" local martingale deflators for a large class of initial models (i.e. models in the small filtration) that are already risk-neutralized. |
| spellingShingle | Choulli, T Aksamit, A Deng, J Jeanblanc, M Non-arbitrage under a class of honest times |
| title | Non-arbitrage under a class of honest times |
| title_full | Non-arbitrage under a class of honest times |
| title_fullStr | Non-arbitrage under a class of honest times |
| title_full_unstemmed | Non-arbitrage under a class of honest times |
| title_short | Non-arbitrage under a class of honest times |
| title_sort | non arbitrage under a class of honest times |
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