Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes

Tommi Sottinen and Lauri Viitasaari ()
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Tommi Sottinen: University of Vaasa
Lauri Viitasaari: Aalto University School of Science, Helsinki

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 590-616

Abstract: 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.

Keywords: Föllmer integral; Gaussian processes; Generalized Lebesgue–Stieltjes integral; Itô–Tanaka formula; Mathematical finance; Pathwise stochastic integral; 60G15; 60H05; 91G20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0588-2

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