  We consider fractional Brownian motion with the Hurst parameters from
(1/2,1). We found that the increment of a fractional Brownian motion can be
represented as the sum of a two independent Gaussian processes one of which is
smooth in the sense that it is differentiable in mean square. We consider
fractional Brownian motion and stochastic integrals generated by the Riemann
sums. As an example of applications, this results is used to find an optimal
pre-programmed strategy in the mean-variance setting for a Bachelier type
market model driven by a fractional Brownian motion.
