Additional utility of insiders with imperfect dynamical information, Finance and Stochastics

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has priv-ileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the infor-mation of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insider’s infor-mation vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.