The minimal entropy measure and an Esscher transform in an incomplete market model
We consider an incomplete market model with one traded stock and two correlated Brownian motions $W$,$\widetilde{W}$. The Brownian motion $W$ drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration $\mathbb{F} := (\widetilde{\mathcal{F}}_{t})_{0 \le t \le T}$ generate...
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| Médium: | Journal article |
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2005
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| _version_ | 1826299229540188160 |
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| author | Monoyios, M |
| author_facet | Monoyios, M |
| author_sort | Monoyios, M |
| collection | OXFORD |
| description | We consider an incomplete market model with one traded stock and two correlated Brownian motions $W$,$\widetilde{W}$. The Brownian motion $W$ drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration $\mathbb{F} := (\widetilde{\mathcal{F}}_{t})_{0 \le t \le T}$ generated by $\widetilde{W}$. We show that the projections of the minimal entropy and minimal martingale measures onto $\widetilde{\mathcal{F}}_{T}$ are related by an Esscher transform involving the correlation between $W$,$\widetilde{W}$, and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an $\widetilde{\mathcal{F}}_{T}$-measurable European claim. |
| first_indexed | 2024-03-07T04:58:44Z |
| format | Journal article |
| id | oxford-uuid:d783c44e-1e03-4b5a-9c4f-0d7cad27e56a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:58:44Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:d783c44e-1e03-4b5a-9c4f-0d7cad27e56a2022-03-27T08:41:43ZThe minimal entropy measure and an Esscher transform in an incomplete market modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d783c44e-1e03-4b5a-9c4f-0d7cad27e56aMathematical Institute - ePrints2005Monoyios, MWe consider an incomplete market model with one traded stock and two correlated Brownian motions $W$,$\widetilde{W}$. The Brownian motion $W$ drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration $\mathbb{F} := (\widetilde{\mathcal{F}}_{t})_{0 \le t \le T}$ generated by $\widetilde{W}$. We show that the projections of the minimal entropy and minimal martingale measures onto $\widetilde{\mathcal{F}}_{T}$ are related by an Esscher transform involving the correlation between $W$,$\widetilde{W}$, and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an $\widetilde{\mathcal{F}}_{T}$-measurable European claim. |
| spellingShingle | Monoyios, M The minimal entropy measure and an Esscher transform in an incomplete market model |
| title | The minimal entropy measure and an Esscher transform in an incomplete market model |
| title_full | The minimal entropy measure and an Esscher transform in an incomplete market model |
| title_fullStr | The minimal entropy measure and an Esscher transform in an incomplete market model |
| title_full_unstemmed | The minimal entropy measure and an Esscher transform in an incomplete market model |
| title_short | The minimal entropy measure and an Esscher transform in an incomplete market model |
| title_sort | minimal entropy measure and an esscher transform in an incomplete market model |
| work_keys_str_mv | AT monoyiosm theminimalentropymeasureandanesschertransforminanincompletemarketmodel AT monoyiosm minimalentropymeasureandanesschertransforminanincompletemarketmodel |