  We consider classical Merton problem of terminal wealth maximization in
finite horizon. We assume that the drift of the stock is following
Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1)
process. In particular, both mean and volatility are unbounded. We assume that
there is Knightian uncertainty on the parameters of both mean and volatility.
We take that the investor has logarithmic utility function, and solve the
corresponding utility maximization problem explicitly. To the best of our
knowledge, this is the first work on utility maximization with unbounded mean
and volatility in Knightian uncertainty under nondominated priors.
