On the Clark-Ocone Theorem for Fractional Brownian Motions with Hurst Parameter bigger than a Half

Abstract

Integration with respect to a fractional Brownian motion with Hurst parameter is related to the inner product: In this paper we provide an example, which shows that multiplication with an indicator function can increase the corresponding norm. We discuss the significance of this result for the quasi-conditional expectation and the fractional Clark-Ocone derivative introduced in Hu and Øksendal [“Fractional White Noise Calculus and Applications to Finance”, IDAQPRT, 6 (2003) 1–32]. Finally, we prove a new version of the fractional Clark-Ocone formula.