| 随机LQ控制在投资组合模型及套期保值问题中的应用 |
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| 引用本文： | 李宏杰,张景军. 随机LQ控制在投资组合模型及套期保值问题中的应用[J]. 工程数学学报, 2008, 25(1): 17-23 |
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| 作者姓名： | 李宏杰 张景军 |
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| 作者单位： | 东华大学信息科学与技术学院,上海,200051;浙江省嘉兴学院数学系,浙江嘉兴,3140011;浙江省嘉兴学院数学系,浙江嘉兴,3140011 |
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| 基金项目： | 浙江省教育厅资助项目(20041121) |
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| 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。
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| 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 |
| 文章编号： | 1005-3085(2008)01-0017-07 |
| 修稿时间： | 2006-02-07 |
Application of Stochastic Linear Quadratic Optimal Control in Portfolio Selection Model and Hedging Strategy Problem |
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| LI Hong-jie,ZHANG Jing-jun. Application of Stochastic Linear Quadratic Optimal Control in Portfolio Selection Model and Hedging Strategy Problem[J]. Chinese Journal of Engineering Mathematics, 2008, 25(1): 17-23 |
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| Authors: | LI Hong-jie ZHANG Jing-jun |
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| Abstract: | 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. |
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| Keywords: | linear quadratic control portfolio Riccati equation hedging strategy Martingmale representation theorem |
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