| 引用本文: | 郭文旌.跳跃扩散股价的最优投资组合选择[J].控制理论与应用,2005,22(2):171~176.[点击复制] |
| GUO Wen-jing.Optimal portfolio selectionwhen stock prices follow jump-diffusion process[J].Control Theory and Technology,2005,22(2):171~176.[点击复制] |
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| 跳跃扩散股价的最优投资组合选择 |
| Optimal portfolio selectionwhen stock prices follow jump-diffusion process |
| 摘要点击 2141 全文点击 2000 投稿时间：2003-06-11 修订日期：2004-02-25 |
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| DOI编号 10.7641/j.issn.1000-8152.2005.2.002 |
| 2005,22(2):171-176 |
| 中文关键词 跳跃扩散过程 最优投资组合 HJB方程 有效前沿 |
| 英文关键词 jump-diffusion process optimal portfolio HJB(Hamilton-Jacobi-Bellman) equation efficient frontier |
| 基金项目 国家自然科学基金资助项目(70471071). |
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| 中文摘要 |
| 假定股票价格服从跳跃扩散过程.在传统均值-方差组合投资模型基础上,最大化最终收益的期望及最小化最终财富的方差.引进一个随机线性二次最优控制问题作为原问题的近似问题.证明了一个状态为跳跃扩散过程的一般最优控制问题的验证性定理.应用验证性定理求解HJB(Hamilton-Jacobi-Bellman)方程得到了原问题的最优策略.最后还给出了原问题有效前沿的表达式. |
| 英文摘要 |
| It is assumed that the stock price follows the jump-diffusion process.In view of the traditional mean-variance portfolio selection model,we maximize the expected terminal return and minimize the variance of the terminal wealth. A stochastic linear-quadratic control problem is introduced as auxiliary problem of the initial problem.A verification theorem for general stochastic optimal control with the state following a jump-diffusion process is showed.By applying verification theorem to the HJB(Hamilton-Jacobi-Bellman) equation,the optimal strategies in an explicit form for initial control problem are presented.Finally,the efficient frontier in a closed form for the original portfolio selection problem is given. |