Applied Mathematics and Optimization

, Volume 42, Issue 1, pp 19–33 | Cite as

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

  • X. Y. Zhou
  • D. Li

Abstract.

This paper is concerned with a continuous-time mean-variance portfolio 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 framework 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 problem.

Key words. Continuous time, Mean-variance, Portfolio, Efficient frontier, Linear-quadratic control. AMS Classification. Primary 90A09, Secondary 93E20. 

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Copyright information

© 2000 Springer-Verlag New York Inc.

Authors and Affiliations

  • X. Y. Zhou
    • 1
  • D. Li
    • 1
  1. 1.Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong xyzhou@se.cuhk.edu.hk, dli@se.cuhk.edu.hk HK

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