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, over(W, ̃). The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration over(F, ̃) {colon equals} (over(F, ̃)t)0 ≤ t ≤ T generated by over(W, ̃). We s...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1826286024509095936 |
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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, over(W, ̃). The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration over(F, ̃) {colon equals} (over(F, ̃)t)0 ≤ t ≤ T generated by over(W, ̃). We show that the projections of the minimal entropy and minimal martingale measures onto over(F, ̃)T are related by an Esscher transform involving the correlation between W, over(W, ̃), and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an over(F, ̃)T-measurable European claim. © 2007 Elsevier B.V. All rights reserved. |
| first_indexed | 2024-03-07T01:37:38Z |
| format | Journal article |
| id | oxford-uuid:95bfa3a5-a154-43de-ae07-09e2cc2bdecd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:37:38Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:95bfa3a5-a154-43de-ae07-09e2cc2bdecd2022-03-26T23:48:16ZThe minimal entropy measure and an Esscher transform in an incomplete market modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:95bfa3a5-a154-43de-ae07-09e2cc2bdecdEnglishSymplectic Elements at Oxford2007Monoyios, MWe consider an incomplete market model with one traded stock and two correlated Brownian motions W, over(W, ̃). The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration over(F, ̃) {colon equals} (over(F, ̃)t)0 ≤ t ≤ T generated by over(W, ̃). We show that the projections of the minimal entropy and minimal martingale measures onto over(F, ̃)T are related by an Esscher transform involving the correlation between W, over(W, ̃), and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an over(F, ̃)T-measurable European claim. © 2007 Elsevier B.V. All rights reserved. |
| 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 |