Mean–variance portfolio selection under partial information with drift uncertainty

ABSTRACT

In this paper, we study the mean–variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not complete and the drift is uncertain. Then, the optimal strategy based on partial information is derived, which reduces to solving a related backward stochastic differential equation (BSDE). Finally, we propose an efficient numerical scheme to approximate the optimal portfolio that is the solution of the BSDE mentioned above. Malliavin calculus and the particle representation play important roles in this scheme.

Keywords:

• Mean–variance portfolio selection
• Malliavin calculus
• Partial information
• Drift uncertainty

JEL Classifications:

• C61
• G11

Acknowledgments

The authors would like to thank two anonymous referees for constructive suggestions that have significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are supported by National Natural Science Foundation of China [grant numbers 61873325, 11831010, 11971409, 11901598]; Southern University of Science and Technology Start up fund [grant number Y01286220]; Hong Kong General Research Fund [grant numbers 15204216, 15202817], and the Hong Kong Polytechnic University.