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Representation formulas for Malliavin derivatives of diffusion processes


  • Jérôme Detemple


  • René Garcia


  • Marcel Rindisbacher



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

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    References listed on IDEAS

    1. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416,
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    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. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    4. 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.
    5. 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.
    6. Dung, Nguyen Tien, 2016. "Tail probability estimates for additive functionals," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 349-356.
    7. 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.
    8. Traian A Pirvu & Ulrich G Haussmann, 2007. "A Portfolio Decomposition Formula," Papers math/0702726,
    9. 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.


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