随机LQ控制在投资组合模型及套期保值问题中的应用  

Application of Stochastic Linear Quadratic Optimal Control in Portfolio Selection Model and Hedging Strategy Problem

作　　者：李宏杰[1] 张景军[2] 

机构地区：[1]东华大学信息科学与技术学院,上海200051 [2]浙江省嘉兴学院数学系,浙江嘉兴314001

出　　处：《工程数学学报》2008年第1期17-23,共7页Chinese Journal of Engineering Mathematics

基　　金：浙江省教育厅资助项目(20041121)

摘　　要：本文提出一类随机线性二次最优控制问题,给出了一个新的Ricatti方程,若此方程有解,可得到系统的最优反馈控制;作为其应用,文中首先讨论了连续时间的投资组合模型,得到最优证券组合;最后将其运用于金融中未定权益的套期保值问题,并得到最优套期保值策略。This paper proposes a general stochastic linear quadratic controllable problem, for which a new stochastic Riccati equation is introduced. If this equation exists solution, the optimal feedback control can be obtained. As an application, we study portfolio selection model with continuous-time and the optimal portfolio is obtained; moreover, hedging strategy problem is studied and the optimal hedging strategy is obtained.

关 键 词：线性二次控制:投资组合 黎卡提方程 套期保值策略 鞅表示定理 

分 类 号：O221.1[理学—运筹学与控制论]