  We investigate Wiener-transformable markets, where the driving process is
given by an adapted transformation of a Wiener process. This includes processes
with long memory, like fractional Brownian motion and related processes, and,
in general, Gaussian processes satisfying certain regularity conditions on
their covariance functions. Our choice of markets is motivated by the
well-known phenomena of the so-called `constant' and `variable depth' memory
observed in real world price processes, for which fractional and
multifractional models are the most adequate descriptions. Motivated by
integral representation results in general Gaussian setting, we study the
conditions under which random variables can be represented as pathwise
integrals with respect to the driving process. From financial point of view, it
means that we give the conditions of replication of contingent claims on such
markets. As an application of our results, we consider the utility maximization
problem in our specific setting. Note that the markets under consideration can
be both arbitrage and arbitrage-free, and moreover, we give the representation
results in terms of bounded strategies.
