# Fractional smoothness and applications in finance

## Author Info

• Stefan Geiss
• Emmanuel Gobet
Registered author(s):

## 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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File URL: http://arxiv.org/pdf/1004.3577

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1004.3577.

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 Length: Date of creation: Apr 2010 Date of revision: Handle: RePEc:arx:papers:1004.3577 Contact details of provider: Web page: http://arxiv.org/

## References

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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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