  We consider the non-adapted version of a simple problem of portfolio
optimization in a financial market that results from the presence of insider
information. We analyze it via anticipating stochastic calculus and compare the
results obtained by means of the Russo-Vallois forward, the Ayed-Kuo, and the
Hitsuda-Skorokhod integrals. We compute the optimal portfolio for each of these
cases with the aim of establishing a comparison between these integrals in
order to clarify their potential use in this type of problem. Our results give
a partial indication that, while the forward integral yields a portfolio that
is financially meaningful, the Ayed-Kuo and the Hitsuda-Skorokhod integrals do
not provide an appropriate investment strategy for this problem.
