Mutual Fund Theorem for continuous time markets with random coefficients

The optimal investment problem is studied for a continuous time incomplete market model. It is assumed that the risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they are independent from the driving Brownian motion, and they are currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities. It is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.