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 .
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. 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 .
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insider information. That is, we
insider information
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. We
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For the latter case we obtain an optimal strategy different from the one computed in Pikovsky and Karatzas. We give various examples for which
In particular, we show that the value of
R
create arbitrage , and for which the logarithmic maximization problem is bounded or unbounded. We conclude with an interesting result, showing
may be bounded while the arbitrage condition holds and we prove
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may not lead to any arbitrage
does not always imply arbitrage for the insider by providing an explicit example