Optimal trading strategy for an investor: the case of partial information

We shall address here the optimization problem of an investor who wants to maximize the expected utility from terminal wealth. The novelty of this paper is that the drift process and the driving Brownian motion appearing in the stochastic differential equation for the security prices are not assumed to be observable for investors in the market. Investors observe security prices and interest rates only. The drift process will be modelled by a Gaussian process, which in a special case becomes a multi-dimensional mean-reverting Ornstein–Uhlenbeck process. The main result of the paper is an explicit representation for the optimal trading strategy for a wide range of utility functions.