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We consider a multi-stock continuous time incomplete market model with randomcoefficients. We study the investment problem in the class of strategies whichdo not use direct observations of the appreciation rates of the stocks, butrather use historical stock prices and an a priory given distribution of theappreciation rates. An explicit solution is found for case of power utilitiesand for a case when the problem can be embedded to a Markovian setting. Somenew estimates and filters for the appreciation rates are given.

Optimal portfolio with unobservable market parameters and certainty equivalence principle