IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v9y2005i3p349-367.html
   My bibliography  Save this article

Representation formulas for Malliavin derivatives of diffusion processes

Author

Listed:
  • Jérôme Detemple
  • René Garcia
  • Marcel Rindisbacher

Abstract

We provide new representation formulas for Malliavin derivatives of diffusions, based on a transformation of the underlying processes. Both the univariate and the multivariate cases are considered. First order as well as higher order Malliavin derivatives are characterized. Numerical illustrations of the benefits of the transformation are provided. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Representation formulas for Malliavin derivatives of diffusion processes," Finance and Stochastics, Springer, vol. 9(3), pages 349-367, July.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:3:p:349-367
    DOI: 10.1007/s00780-004-0151-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-004-0151-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-004-0151-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Neuenkirch, Andreas, 2008. "Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2294-2333, December.
    2. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    4. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    5. Christian Olivera & Evelina Shamarova, 2020. "Gaussian density estimates for solutions of fully coupled forward‐backward SDEs," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1554-1564, August.
    6. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    7. Detemple, Jerome & Garcia, Rene & Rindisbacher, Marcel, 2006. "Asymptotic properties of Monte Carlo estimators of diffusion processes," Journal of Econometrics, Elsevier, vol. 134(1), pages 1-68, September.
    8. Dung, Nguyen Tien, 2016. "Tail probability estimates for additive functionals," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 349-356.
    9. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    10. Marc Lagunas-Merino & Salvador Ortiz-Latorre, 2020. "A decomposition formula for fractional Heston jump diffusion models," Papers 2007.14328, arXiv.org.
    11. Nguyen, Tien Dung, 2018. "Tail estimates for exponential functionals and applications to SDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4154-4170.
    12. Likibi Pellat, Rhoss & Menoukeu Pamen, Olivier, 2024. "Density analysis for coupled forward–backward SDEs with non-Lipschitz drifts and applications," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    13. Traian A Pirvu & Ulrich G Haussmann, 2007. "A Portfolio Decomposition Formula," Papers math/0702726, arXiv.org.
    14. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:9:y:2005:i:3:p:349-367. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.