Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes |
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| Authors: | Tommi Sottinen Lauri Viitasaari |
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| Institution: | 1.Department of Mathematics and Statistics,University of Vaasa,Vaasa,Finland;2.Department of Mathematics and System Analysis,Aalto University School of Science, Helsinki,Aalto,Finland;3.Department of Mathematics,Saarland University, Saarbrücken,Saarbrücken,Germany |
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| 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. |
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