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

被引:689
作者
Zhou, XY [1 ]
Li, D [1 ]
机构
[1] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
关键词
continuous time; mean-variance; portfolio; efficient frontier; linear-quadratic control;
D O I
10.1007/s002450010003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:19 / 33
页数:15
相关论文
共 30 条
[1]  
Anderson B.D.O., 1989, Optimal Control: Linear Quadratic Methods
[2]  
[Anonymous], FINANCE DYNAMIC PROC
[3]  
BENSOUSSAN A, 1982, LECT NOTES MATH, V972, P1
[4]  
CHEN S, IN PRESS SIAM J CONT
[5]   Stochastic linear quadratic regulators with indefinite control weight costs [J].
Chen, SP ;
Li, XJ ;
Zhou, XY .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (05) :1685-1702
[6]  
Duffie D., 1991, Ann. Appl. Probab., V1, P1, DOI DOI 10.1214/AOAP/1177005978
[7]   AN EXACT SOLUTION TO A DYNAMIC PORTFOLIO CHOICE PROBLEM UNDER TRANSACTIONS COSTS [J].
DUMAS, B ;
LUCIANO, E .
JOURNAL OF FINANCE, 1991, 46 (02) :577-595
[8]  
FLEMING W. H., 2005, Stochastic Modelling and Applied Probability, V2nd
[9]  
Follmer H., 1986, Contributions to Mathematical Economics
[10]  
Francis J. C., 1976, INVESTMENTS ANAL MAN