Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911873192951808 |
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| author | Lepinette, Emmanuel Vu, Duc Thinh |
| author_facet | Lepinette, Emmanuel Vu, Duc Thinh |
| contents | The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on $L^0$ is fixed to characterize the family of acceptable wealths that play the role of non negative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices (called risk-hedging prices) of a European option. Moreover, we show that the set of all risk-hedging prices is closed under NA. At last, we provide a dual representation of the risk-measure on $L^0$ under some conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation Lepinette, Emmanuel Vu, Duc Thinh Risk Management Probability The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on $L^0$ is fixed to characterize the family of acceptable wealths that play the role of non negative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices (called risk-hedging prices) of a European option. Moreover, we show that the set of all risk-hedging prices is closed under NA. At last, we provide a dual representation of the risk-measure on $L^0$ under some conditions. |
| title | Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation |
| topic | Risk Management Probability |
| url | https://arxiv.org/abs/2405.06764 |