Pathwise integrals and Ito-Tanaka Formula for Gaussian processes

Tommi Sottinen; Lauri Viitasaari

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arXiv · 1307.3578

Pathwise integrals and Ito-Tanaka Formula for Gaussian processes

Tommi Sottinen·Lauri Viitasaari

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Abstract

We prove the Ito-Tanaka formula and the 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 F\"ollmer and as pathwise generalized Lebesgue-Stieltjes integrals introduced by Z\"ahle. As an application, we illustrate the importance of Ito-Tanaka formula for pricing and hedging of financial derivatives.

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Tommi Sottinen, Lauri Viitasaari. 2013-07-12. Pathwise integrals and Ito-Tanaka Formula for Gaussian processes. https://arxiv.org/abs/1307.3578

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