Journal of Theoretical Probability

, Volume 29, Issue 2, pp 590–616 | Cite as

Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes



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.


Föllmer integral Gaussian processes Generalized Lebesgue–Stieltjes integral Itô–Tanaka formula Mathematical finance Pathwise stochastic integral 

Mathematics Subject Classification 2010

60G15 60H05 91G20 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VaasaVaasaFinland
  2. 2.Department of Mathematics and System AnalysisAalto University School of Science, HelsinkiAaltoFinland
  3. 3.Department of MathematicsSaarland University, SaarbrückenSaarbrückenGermany

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