Pathwise integrals and Ito-Tanaka Formula for Gaussian processes

TL;DR

This paper establishes the Ito-Tanaka formula and pathwise stochastic integrals for broad classes of Gaussian processes, with applications in financial derivative pricing and hedging.

Contribution

It introduces new methods for defining stochastic integrals for Gaussian processes and proves the Ito-Tanaka formula in this context.

Findings

Proves Ito-Tanaka formula for Gaussian processes

Defines pathwise stochastic integrals using Föllmer and Zähle approaches

Demonstrates applications in financial derivatives pricing

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.