Quantitative Fundamental Theorem of Asset Pricing
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911747831496704 |
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| author | Acciaio, Beatrice Backhoff, Julio Pammer, Gudmund |
| author_facet | Acciaio, Beatrice Backhoff, Julio Pammer, Gudmund |
| contents | In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15037 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantitative Fundamental Theorem of Asset Pricing Acciaio, Beatrice Backhoff, Julio Pammer, Gudmund Mathematical Finance 60G48, 91G15, 49Q22 In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance. |
| title | Quantitative Fundamental Theorem of Asset Pricing |
| topic | Mathematical Finance 60G48, 91G15, 49Q22 |
| url | https://arxiv.org/abs/2209.15037 |