Additional Utility of Insiders with Imperfect Dynamical Information
UPF Economics and Business Working Paper No. 675
28 Pages Posted: 8 Sep 2003
Date Written: April 4, 2003
In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every trader. Our financial markets are based on Wiener space. In probabilistic terms we obtain an infinite dimensional extension of Jacod's theorem to cover cases of progressive enlargement of filtrations. The application of this result gives the semimartingale decomposition of the original Wiener process under the progressively enlarged filtration. As an application we prove that if the rate at which the additional noise in the insider's information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.
Keywords: Insider trading, enlargement of filtrations, Malliavin's calculus, utility maximization, arbitrage
JEL Classification: G140
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