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Within the well-known framework of financial portfolio optimization, weanalyze the existing relationships between the condition of arbitrage and theutility maximization in presence of \emph{insider information}. We assume that,since the initial time, the information flow is altered by adding the knowledgeof an additional random variable including future information. In this contextwe study the utility maximization problem under the logarithmic and theConstant Relative Risk Aversion (CRRA) utilities, with and without therestriction of no temporary-bankruptcy. In particular, we show that the valueof the insider information may be bounded while the arbitrage condition holdsand we prove that the insider information does not always imply arbitrage forthe insider by providing an explicit example.

Insider information and its relation with the arbitrage condition and the utility maximization problem