Quasi-sure essential supremum and applications to finance
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916161555267584 |
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| author | Carassus, Laurence |
| author_facet | Carassus, Laurence |
| contents | When uncertainty is modelled by a set of non-dominated and non-compact probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the properties postulated on the initial functions carry over to their quasi-sure essential supremum. We propose various applications to financial problems with frictions. We analyse super-replication and prove a bi-dual characterization of the super-hedging cost. We also study a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. This requires new results on the aggregation of quasi-sure statements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12862 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasi-sure essential supremum and applications to finance Carassus, Laurence Mathematical Finance When uncertainty is modelled by a set of non-dominated and non-compact probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the properties postulated on the initial functions carry over to their quasi-sure essential supremum. We propose various applications to financial problems with frictions. We analyse super-replication and prove a bi-dual characterization of the super-hedging cost. We also study a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. This requires new results on the aggregation of quasi-sure statements. |
| title | Quasi-sure essential supremum and applications to finance |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2107.12862 |