  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.
