Exponential utility maximization with delay in a continuous time Gaussian framework

In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the risky asset's price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case where the risky asset is given by a Gaussian process (with some additional properties) we establish a solution for the optimal control and the corresponding value. Our approach is purely probabilistic and is based on the theory for Radon–Nikodym derivatives of Gaussian measures developed by Shepp (1966) and Hitsuda (1968).