Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. That is, we assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy. For the latter case we obtain an optimal strategy different from the one computed in Pikovsky and Karatzas. We give various examples for which the insider information create arbitrage, and for which the logarithmic maximization problem is bounded or unbounded. We conclude with an interesting result, showing that the insider information may not lead to any arbitrage.
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