Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework |
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Authors: | X Y Zhou D Li |
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Institution: | (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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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.
Accepted 24 November 1999 |
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Keywords: | , Continuous time, Mean-variance, Portfolio, Efficient frontier, Linear-quadratic control, AMS Classification, Primary,,,,,90A09, Secondary 93E20, |
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