The functional Itō formula under the family of continuous semimartingale measures
Dupire [16] introduced a notion of smoothness for functionals of paths and arrived at a generalization of Itō’s formula that applies to functionals with a continuous dependence on the trajectories of the underlying process. In this paper, we study nonlinear functionals that do not have such continui...
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| Natura: | Journal article |
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World Scientific Publishing
2015
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| _version_ | 1826267730134695936 |
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| author | Oberhauser, H |
| author_facet | Oberhauser, H |
| author_sort | Oberhauser, H |
| collection | OXFORD |
| description | Dupire [16] introduced a notion of smoothness for functionals of paths and arrived at a generalization of Itō’s formula that applies to functionals with a continuous dependence on the trajectories of the underlying process. In this paper, we study nonlinear functionals that do not have such continuity. By revisiting old work of Bichteler and Karandikar we show that one can construct pathwise versions of complex functionals like the quadratic variation, stochastic integrals or Itō processes that are still regular enough such that a functional Itō-formula applies. |
| first_indexed | 2024-03-06T20:58:40Z |
| format | Journal article |
| id | oxford-uuid:3a21c3be-2b5f-4ef3-821e-34e1a67976a1 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:58:40Z |
| publishDate | 2015 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:3a21c3be-2b5f-4ef3-821e-34e1a67976a12022-03-26T13:59:38ZThe functional Itō formula under the family of continuous semimartingale measuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a21c3be-2b5f-4ef3-821e-34e1a67976a1Symplectic Elements at OxfordWorld Scientific Publishing2015Oberhauser, HDupire [16] introduced a notion of smoothness for functionals of paths and arrived at a generalization of Itō’s formula that applies to functionals with a continuous dependence on the trajectories of the underlying process. In this paper, we study nonlinear functionals that do not have such continuity. By revisiting old work of Bichteler and Karandikar we show that one can construct pathwise versions of complex functionals like the quadratic variation, stochastic integrals or Itō processes that are still regular enough such that a functional Itō-formula applies. |
| spellingShingle | Oberhauser, H The functional Itō formula under the family of continuous semimartingale measures |
| title | The functional Itō formula under the family of continuous semimartingale measures |
| title_full | The functional Itō formula under the family of continuous semimartingale measures |
| title_fullStr | The functional Itō formula under the family of continuous semimartingale measures |
| title_full_unstemmed | The functional Itō formula under the family of continuous semimartingale measures |
| title_short | The functional Itō formula under the family of continuous semimartingale measures |
| title_sort | functional ito formula under the family of continuous semimartingale measures |
| work_keys_str_mv | AT oberhauserh thefunctionalitoformulaunderthefamilyofcontinuoussemimartingalemeasures AT oberhauserh functionalitoformulaunderthefamilyofcontinuoussemimartingalemeasures |