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