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Optimal Approximation of Skorohod Integrals

Author

Listed:
  • Andreas Neuenkirch

    (University of Mannheim)

  • Peter Parczewski

    (University of Mannheim)

Abstract

In this manuscript, we determine the optimal approximation rate for Skorohod integrals of sufficiently regular integrands. This generalizes the optimal approximation results for Itô integrals. However, without adaptedness and the Itô isometry, new proof techniques are required. The main tools are a characterization via S-transform and a reformulation of the Wiener chaos decomposition in terms of Wick-analytic functionals.

Suggested Citation

  • Andreas Neuenkirch & Peter Parczewski, 2018. "Optimal Approximation of Skorohod Integrals," Journal of Theoretical Probability, Springer, vol. 31(1), pages 206-231, March.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0716-2
    DOI: 10.1007/s10959-016-0716-2
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    References listed on IDEAS

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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Chen, Nan & Glasserman, Paul, 2007. "Malliavin Greeks without Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1689-1723, November.
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