Abstract We work with fractional Brownian motion with Hurst index H 1/2. We show that the pricing model based on geometric fractional Brownian motion behaves to certain extend as a process with bounded variation. This observation is based on a new change of variables formula for a convex...

The aim of this paper is to give an extension of the mean-variance hedging problem to the $\mathcal{L}^p$-setting, where 1 p ∞. Remark that the mean-variance hedging is corresponding to the case where p = 2. Firstly, we prove that the unique existence of the optimal hedging strategy in the...

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the...