Conditional-mean hedging under transaction costs in Gaussian models

Abstract

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black–Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.