Portfolio Optimization with Information Asymmetry

This chapter focuses on the characterization and simulation of the optimal strategy of investors that possess some side-information about the market structure, with the purpose of comparing it with non-insider’s optimal strategy. The investors strive to maximize their expected discounted utility of terminal wealth on [0, T ], where T  > 0 is a fixed finite time horizon. The investors observe the same stock prices, but their total information may differ due to some extra information that has been obtained in some other way. This is naturally related to the enlargement of filtration problem. As mathematically, the problem is determining the semimartingale decomposition of the Wiener and the Poisson processes in the filtration enlarged with the additional information of the insider, leading to the computation of the so-called information drift. Thus, we can express the dynamics of the prices for this insider and compute her optimal investment strategy.