🤖 AI Summary
This paper addresses the exponential utility maximization problem for an investor operating in a continuous-time Gaussian framework with delayed price observations—a non-Markovian stochastic control problem. Methodologically, the authors employ a purely probabilistic approach, integrating Radon–Nikodym derivatives, equivalence of Gaussian measures, stochastic filtering, and optimal control theory. They derive closed-form expressions for both the optimal investment strategy and the value function, rigorously establishing existence and uniqueness of the solution. Their work unifies and extends the Shepp–Hitsuda measure transformation theory to settings involving observation delay and Gaussian dynamics. The results quantitatively characterize how information latency distorts portfolio composition—specifically, inducing time-dependent feedback gains and altering the effective signal-to-noise ratio in the control law. This provides a tractable, analytically solvable paradigm for non-Markovian utility optimization under partial and delayed information.
📝 Abstract
In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the 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 cite{S:66}, Hitsuda cite{H:68} and received a new and unifying angle in [2].
