Advanced search
Publication Cover
Stochastic Analysis and Applications Volume 28, 2010 - Issue 6
Submit an article Journal homepage
188
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

White Noise Generalization of the Clark-Ocone Formula Under Change of Measure

Yeliz Yolcu Okur Centre of Mathematics for Applications (CMA), Institute of Mathematics, University of Oslo, Oslo, Norway; Institute of Applied Mathematics, Middle East Technical University, Ankara, TurkeyCorrespondence[email protected]
Pages 1106-1121 | Received 29 Sep 2009, Accepted 29 Sep 2009, Published online: 29 Oct 2010

References

  • Aase , K. , Øksendal , B. , Privault , N. , and Ubøe , J. 2000 . White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance . Finance and Stochastic 4 : 465 – 496 .
  • Aase , K. , Øksendal , B. , and Ubøe , J. 2001 . Donsker delta function to compute hedging strategies . Potential Analysis 14 : 351 – 374 .
  • Benth , F.E. , and Potthoff , J. 1996 . On the martingale property for generalized stochastic processes . Stochastic and Stochastic Reports 58 : 349 – 367 .
  • Clark , J.M.C. 1970 . The representation of functionals of Brownian motion by stochastic integrals . Annals of Mathematical and Statistics 41 : 1282 – 1295 .
  • Di Nunno , G. , Øksendal, B., and Proske , P. 2009 . Malliavin Calculus for Lévy Processes with Applications to Finance . Springer-Verlag , New York .
  • Hida , T. 1980 . Brownian Motion . Springer-Verlag , New York .
  • Hida , T. 1982 . White noise analysis and its applications. In Proceedings of International Mathematics Conference. Chen, L.H.Y. et al., (eds.), North-Holland, Amsterdam, pp. 43–48.
  • Hida , T. , Kuo H., Potthoff , J. , and Streit , L. 1993 . White Noise, An Infinite Dimensional Approach . Kluwer , New York .
  • Holden , H. , Øksendal B. , Ubøe , J. , Zhang , T. 1996 . Stochastic Partial Differential Equations . Birkhäuser , Boston .
  • Hu , Y. , and Øksendal , B. 2003 . Fractional white noise calculus and applications to finance . Inf. Dim. Analysis and Quantum Prob. Related Topics 6 : 1 – 32 .
  • Itô , K. 1951 . Multiple wiener integral . Journal of Mathematical Society of Japan 3 : 157 – 169 .
  • Karatzas , I. , and Ocone , D. 1991 . A generalized clark representation formula, with application to optimal portfolios . Stochastics and Stochastic Reports 34 : 187 – 220 .
  • Karatzas , I. , and Shreve , S. 1987. Brownian Motion and Stochastic Calculus . Springer-Verlag , New York.
  • Loève , M. 1978 . Probability Theory II . Springer-Verlag , New York .
  • Ocone , D. 1984 . Malliavin calculus and stochastic integral representations of diffusion processes . Stochastics 12 : 161 – 185 .
  • Potthoff , J. , and Timpel , M. 1995 . On a dual pair of spaces of smooth and generalized random variables . Potential Analysis 4 : 637 – 654 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.