Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift

TL;DR

This paper analyzes the conditions under which utility maximization problems in financial markets with hidden Gaussian drifts are well posed, focusing on the impact of unbounded processes and utility function bounds.

Contribution

It provides new sufficient conditions on model parameters ensuring bounded maximum expected utility in markets with partial information and Gaussian drift processes.

Findings

Derived conditions for bounded utility with power utility functions.

Identified restrictions on model parameters like investment horizon and variance.

Extended results to both full and partial information scenarios.

Abstract

This paper investigates well posedness of utility maximization problems for financial markets where stock returns depend on a hidden Gaussian mean reverting drift process. Since that process is potentially unbounded, well posedness cannot be guaranteed for utility functions which are not bounded from above. For power utility with relative risk aversion smaller than that of log-utility this leads to restrictions on the choice of model parameters such as the investment horizon and parameters controlling the variance of the asset price and drift processes. We derive sufficient conditions to the model parameters leading to bounded maximum expected utility of terminal wealth for models with full and partial information.