  We consider a multi-stock continuous time incomplete market model with random
coefficients. We study the investment problem in the class of strategies which
do not use direct observations of the appreciation rates of the stocks, but
rather use historical stock prices and an a priory given distribution of the
appreciation rates. An explicit solution is found for case of power utilities
and for a case when the problem can be embedded to a Markovian setting. Some
new estimates and filters for the appreciation rates are given.
