  We consider a financial market model driven by an R^n-valued Gaussian process
with stationary increments which is different from Brownian motion. This
driving noise process consists of $n$ independent components, and each
component has memory described by two parameters. For this market model, we
explicitly solve optimal investment problems. These include (i) Merton's
portfolio optimization problem; (ii) the maximization of growth rate of
expected utility of wealth over the infinite horizon; (iii) the maximization of
the large deviation probability that the wealth grows at a higher rate than a
given benchmark. The estimation of paremeters is also considered.
