随机线性二次最优控制在投资组合中的应用  

Application of stochastic linear quadratic optimal control in portfolio selection problem

作　　者：李宏杰[1] 杨晓春[1] 

机构地区：[1]嘉兴学院数学系,浙江嘉兴314001

出　　处：《系统工程学报》2007年第5期461-466,473,共7页Journal of Systems Engineering

基　　金：浙江省教育厅资助项目(20041121)

摘　　要：提出一类随机线性二次最优控制问题,给出了一个新的随机黎卡提方程,若此方程有解,就可以得到系统的最优反馈控制;作为其应用,讨论了连续时间的均值-方差投资组合选择问题,其目标是投资组合的最终收益最大,风险最小,通过"嵌入"方法将其转化为随机线性二次最优控制问题,并在非自融资的条件下,得出最优证券组合;最后将其理论应用于实例分析.This paper gives a class of stochastic linear quadratic control problem, a new stochastic Riceati equation is introduced, and if this equation exists solution, the optimal feedback control of system can be obtained. As its application, this paper studies class of mean-variance portfolio selection problem with continuous-time, its objective is to minimize the expected terminal return and minimize the variance of the terminal wealth, the problem can he transformed into a stochastic linear quadratic controle problem by the way of embedded. Moreover, the optimal portfolio is obtained under the condition of non-self-financing, and an example is given at last.

关 键 词：线性二次控制 均值一方差 投资组合 随机黎卡提方程 

分 类 号：O29[理学—应用数学] F224[理学—数学]