Appl Math Optim 42:19–33 (2000)
2000 Springer-Verlag New York Inc.
Continuous-Time Mean-Variance Portfolio Selection:
A Stochastic LQ Framework
X. Y. Zhou and D. Li
Department of Systems Engineering and Engineering Management,
The Chinese University of Hong Kong,
Shatin, Hong Kong
Communicated by M. Nisio
Abstract. This paper is concerned with a continuous-time mean-variance port-
folio selection model that is formulated as a bicriteria optimization problem. The
objective is to maximize the expected terminal return and minimize the variance
of the terminal wealth. By putting weights on the two criteria one obtains a single
objective stochastic control problem which is however not in the standard form
due to the variance term involved. It is shown that this nonstandard problem can
be “embedded” into a class of auxiliary stochastic linear-quadratic (LQ) problems.
The stochastic LQ control model proves to be an appropriate and effective frame-
work to study the mean-variance problem in light of the recent development on
general stochastic LQ problems with indeﬁnite control weighting matrices. This
gives rise to the efﬁcient frontier in a closed form for the original portfolio selection
KeyWords. Continuoustime,Mean-variance,Portfolio, Efﬁcientfrontier,Linear-
AMS Classiﬁcation. Primary 90A09, Secondary 93E20.
This research was supported by the RGC Earmarked Grants CUHK 4125/97E, CUHK 4054/98E, and