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Fractional Smoothness and Applications in Finance

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Advanced Mathematical Methods for Finance

Abstract

This overview article concerns the notion of fractional smoothness of random variables of the form g(X T ), where X=(X t ) t∈[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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Notes

  1. 1.

    Here again, the boundedness assumptions on g can be weakened, and we refer to the original papers.

  2. 2.

    With T=1, we are in accordance with the quoted literature that used Hermite polynomials. Of course, we could do a rescaling to T>0 afterwards.

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Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, Technikerstraße 13/7, 6020, Innsbruck, Austria

    Stefan Geiss

  2. Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 38041, Grenoble Cedex 9, France

    Emmanuel Gobet

Authors
  1. Stefan Geiss
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  2. Emmanuel Gobet
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Correspondence to Stefan Geiss .

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Editors and Affiliations

  1. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Giulia Di Nunno

  2. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Bernt Øksendal

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Geiss, S., Gobet, E. (2011). Fractional Smoothness and Applications in Finance. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_12

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