Mutual fund theorem for continuous time markets with random coefficients

Abstract

The optimal investment problem is studied for acontinuous time incomplete market model. It is assumed that therisk-free rate, the appreciation rates and the volatility of thestocks are all random; they are independent from the drivingBrownian motion, and they are currently observable. It is shownthat some weakened version of Mutual Fund Theorem holds for thismarket for general class of utilities. It is shown that the supremumof expected utilities can be achieved on a sequence of strategieswith a certain distribution of risky assets that does not depend onrisk preferences described by different utilities.