Additional utility of insiders with imperfect dynamical information

In this paper we consider an insider with privileged information thatis affected by an independent noise vanishing as the revelation timeapproaches. At this time, information is available to every trader. Ourfinancial markets are based on Wiener space. In probabilistic terms weobtain an infinite dimensional extension of Jacod s theorem to covercases of progressive enlargement of filtrations. The application ofthis result gives the semimartingale decomposition of the originalWiener process under the progressively enlarged filtration. As anapplication we prove that if the rate at which the additional noise inthe insider s information vanishes is slow enough then there is noarbitrage and the additional utility of the insider is finite.