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Malliavin differentiability of indicator functions on canonical Lévy spaces

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  • Suzuki, Ryoichi

Abstract

In this paper, we consider Malliavin differentiability of indicator functions on canonical Lévy spaces. We give necessary and sufficient conditions for it. This is a Lévy space version of a result of Sekiguchi and Shiota (1985).

Suggested Citation

  • Suzuki, Ryoichi, 2018. "Malliavin differentiability of indicator functions on canonical Lévy spaces," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 183-190.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:183-190
    DOI: 10.1016/j.spl.2018.01.024
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    References listed on IDEAS

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    1. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2017. "Local risk-minimization for Barndorff-Nielsen and Shephard models," Finance and Stochastics, Springer, vol. 21(2), pages 551-592, April.
    2. Elisa Alòs & Jorge A. León & Monique Pontier & Josep Vives, 2008. "A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility," Economics Working Papers 1081, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
    4. Solé, Josep Lluís & Utzet, Frederic & Vives, Josep, 2007. "Canonical Lévy process and Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 165-187, February.
    5. Delong, Lukasz & Imkeller, Peter, 2010. "On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1748-1775, August.
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