In this paper we consider a financial market with an insider that has, at time t = 0, some additional information of the whole developing of the market. We use the forward integral, which is an anticipating integral, and the techniques of the Malliavin calculus so that we can take advantage of the privileged information to maximize the expected logarithmic utility from terminal wealth.KEY WORDS: derivative operator in the Malliavin calculus sense, forward and Skorohod integrals, optimal portfolio, expected utility