  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 \emph{insider information}. 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. In particular, we show that the value
of the insider information may be bounded while the arbitrage condition holds
and we prove that the insider information does not always imply arbitrage for
the insider by providing an explicit example.
