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A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis

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  • Jirô Akahori

    (Ritsumeikan University)

  • Takafumi Amaba

    (Ritsumeikan University)

  • Kaori Okuma

    (Ritsumeikan University)

Abstract

In this paper, we will establish a discrete-time version of Clark(–Ocone–Haussmann) formula, which can be seen as an asymptotic expansion in a weak sense. The formula is applied to the estimation of the error caused by the martingale representation. Throughout, we use another distribution theory with respect to Gaussian rather than Lebesgue measure, which can be seen as a discrete Malliavin calculus.

Suggested Citation

  • Jirô Akahori & Takafumi Amaba & Kaori Okuma, 2017. "A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis," Journal of Theoretical Probability, Springer, vol. 30(3), pages 932-960, September.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:3:d:10.1007_s10959-016-0666-8
    DOI: 10.1007/s10959-016-0666-8
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    References listed on IDEAS

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    1. E. Temam, 2003. "Analysis of Error with Malliavin Calculus: Application to Hedging," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 201-214, January.
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    3. Takaki Hayashi & Per A. Mykland, 2005. "Evaluating Hedging Errors: An Asymptotic Approach," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 309-343, April.
    4. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    5. Geiss, Christel & Geiss, Stefan & Gobet, Emmanuel, 2012. "Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2078-2116.
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    Cited by:

    1. Tsubasa Nishimura & Kenji Yasutomi & Tomooki Yuasa, 2022. "Higher-Order Error Estimates of the Discrete-Time Clark–Ocone Formula," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2518-2539, December.

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