摘要
研究在证券价格服从一个带有随机方差几何布朗运动情况下的最优消费和投资问题。首先建立了最优消费和投资问题随机最优控制数学模型 ,运用随机最优控制理论 ,得到了最优消费和投资随机最优控制问题的值函数所满足的偏微分方程 ;其次 ,基于最优控制问题的值函数给出了具有反馈形式的最优消费和投资策略 ,并与经典Merton问题进行了比较分析 ;最后 ,进行了算例分析。
This paper researches the optimal consumption and investment decision problem when the securities prices follow geometric Brownian motion with stochastic volatility. First,the stochastic optimal control model for the optimal consumption and investment decision problem was established. Second,the partial differential equation was obtained for the value function by using stochastic optimal control theory. Third,the paper gives the optimal consumption and investment tactics with feed-back form,based on the value function of the stochastic optimal control problem,and it compare with classical Merton problem. Finally,an example is provided.
出处
《管理工程学报》
CSSCI
2002年第1期47-50,共4页
Journal of Industrial Engineering and Engineering Management
基金
国家自然科学基金资助项目 ( 70 1730 31)
国家杰出青年科学基金资助项目 ( 70 0 2 5 30 3)
