Continuous-time mean-variance portfolio selection : A stochastic LQ framework

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Original languageEnglish
Pages (from-to)19-33
Journal / PublicationApplied Mathematics and Optimization
Issue number1
Publication statusPublished - Jan 2000
Externally publishedYes


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.