A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty
We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to wo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-10-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2227-9091/2/4/425 |
| _version_ | 1818542315720933376 |
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| author | Erhan Bayraktar Yuchong Zhang Zhou Zhou |
| author_facet | Erhan Bayraktar Yuchong Zhang Zhou Zhou |
| author_sort | Erhan Bayraktar |
| collection | DOAJ |
| description | We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting. |
| first_indexed | 2024-12-11T22:20:28Z |
| format | Article |
| id | doaj.art-2467759edc59463caf31a557774d3000 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-11T22:20:28Z |
| publishDate | 2014-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-2467759edc59463caf31a557774d30002022-12-22T00:48:27ZengMDPI AGRisks2227-90912014-10-012442543310.3390/risks2040425risks2040425A Note on the Fundamental Theorem of Asset Pricing under Model UncertaintyErhan Bayraktar0Yuchong Zhang1Zhou Zhou2Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USADepartment of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USADepartment of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USAWe show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.http://www.mdpi.com/2227-9091/2/4/425Model uncertaintybid-ask prices for optionssemi-static hedgingnon-dominated collection of probability measuresFundamental Theorem of Asset Pricingsuper-hedgingrobust no-arbitragenon-redundant options |
| spellingShingle | Erhan Bayraktar Yuchong Zhang Zhou Zhou A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty Risks Model uncertainty bid-ask prices for options semi-static hedging non-dominated collection of probability measures Fundamental Theorem of Asset Pricing super-hedging robust no-arbitrage non-redundant options |
| title | A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty |
| title_full | A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty |
| title_fullStr | A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty |
| title_full_unstemmed | A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty |
| title_short | A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty |
| title_sort | note on the fundamental theorem of asset pricing under model uncertainty |
| topic | Model uncertainty bid-ask prices for options semi-static hedging non-dominated collection of probability measures Fundamental Theorem of Asset Pricing super-hedging robust no-arbitrage non-redundant options |
| url | http://www.mdpi.com/2227-9091/2/4/425 |
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