Mean‐Variance Portfolio Selection under Partial Information

Abstract

This paper is concerned with a continuous‐time mean‐variance portfolio selection problem in a (possibly incomplete) market with multiple stocks and a bond. Only the past price movements of the stocks and the bond are the information available to the investors. A separation principle is shown to hold in this setting. Efficient strategies based on the aforementioned partial information are derived, which involve the optimal filter of the stock appreciation rate processes. The main methodological contribution of the paper is to employ the particle system representation to develop analytical and numerical approaches in obtaining the filter as well as solving the related backward stochastic differential equation.