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Fractional smoothness and applications in finance

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  • Stefan Geiss
  • Emmanuel Gobet

Abstract

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.

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  • Stefan Geiss & Emmanuel Gobet, 2010. "Fractional smoothness and applications in finance," Papers 1004.3577, arXiv.org.
  • Handle: RePEc:arx:papers:1004.3577
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    File URL: http://arxiv.org/pdf/1004.3577
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    References listed on IDEAS

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    1. Geiss, Christel & Geiss, Stefan, 2006. "On an approximation problem for stochastic integrals where random time nets do not help," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 407-422, March.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
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