Additional utility of insiders with imperfect dynamical information
The authors consider a market driven by a Wiener process where there is an insider and a regular trader. They propose to study situations in which the insider knows a functional of the underlying process deformed by an independent noise, which vanishes as revelation time \(T\) approaches. This has obvious relations with the actual evolution of information in markets. Mathematically, this shows the need to develop a dynamical enlargement of filtrations. Using Malliavin calculus, the authors obtain the semimartingale decomposition of the original Wiener process under such dynamical enlargement of filtration. Results in all examples state that if the rate at which blurring noise disappears is sufficiently slow, then there is a finite additional logarithmic utility and no arbitrage. Therefore, this allows a construction of a stable market where insiders and regular traders coexist.
scientific article; zbMATH DE number 2169543
scientific article