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Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes

Author

Listed:
  • Tommi Sottinen

    (University of Vaasa)

  • Lauri Viitasaari

    (Aalto University School of Science, Helsinki
    Saarland University, Saarbrücken)

Abstract

We prove an Itô–Tanaka formula and existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by Föllmer and as pathwise generalized Lebesgue–Stieltjes integrals introduced by Zähle. As an application, we illustrate the importance of the Itô–Tanaka formula for pricing and hedging of financial derivatives.

Suggested Citation

  • Tommi Sottinen & Lauri Viitasaari, 2016. "Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 590-616, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0588-2
    DOI: 10.1007/s10959-014-0588-2
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    References listed on IDEAS

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    1. Coutin, Laure & Nualart, David & Tudor, Ciprian A., 2001. "Tanaka formula for the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 301-315, August.
    2. Dieter Sondermann, 2006. "Introduction to Stochastic Calculus for Finance," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-34837-5, October.
    3. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
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