Journal article
The functional Itō formula under the family of continuous semimartingale measures
- Abstract:
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, pdf, 359.9KB, Terms of use)
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- Publisher copy:
- 10.1142/S0219493716500106
Authors
- Publisher:
- World Scientific Publishing
- Journal:
- Stochastics and Dynamics More from this journal
- Volume:
- 16
- Issue:
- 04
- Pages:
- ARTN 1650010
- Publication date:
- 2015-10-06
- Acceptance date:
- 2015-09-28
- DOI:
- EISSN:
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1793-6799
- ISSN:
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0219-4937
- Keywords:
- Pubs id:
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pubs:548173
- UUID:
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uuid:3a21c3be-2b5f-4ef3-821e-34e1a67976a1
- Local pid:
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pubs:548173
- Source identifiers:
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548173
- Deposit date:
-
2018-03-21
Terms of use
- Copyright holder:
- World Scientific Publishing
- Copyright date:
- 2015
- Notes:
- © 2015 World Scientific Publishing Co Pte Ltd. This is the accepted manuscript version of the article. The final version is available online from World Scientific Publishing at: https://doi.org/10.1142/S0219493716500106
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