We study the optimal investment problem for a continuous time incomplete
market model such that the risk-free rate, the appreciation rates and the
volatility of the stocks are all random; they are assumed to be independent
from the driving Brownian motion, and they are supposed to be currently
observable. It is shown that some weakened version of Mutual Fund Theorem holds
for this market for general class of utilities; more precisely, 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.Comment: 17 page
