含有随机波动的非线性的最优投资和消费模型  

Non-linear Optimal Investment and Consumption Model with Stochastic Volatility

作　　者：胡世培[1] 肖建武[2] 

机构地区：[1]浙江林学院数学系,杭州311300 [2]中南林业科技大学商学院,长沙410004

出　　处：《应用数学与计算数学学报》2009年第1期1-12,共12页Communication on Applied Mathematics and Computation

摘　　要：在连续时间模型假设下,研究风险资产价格服从一个带有随机波动的几何布朗运动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;然后运用随机最优控制理论,得到了最优投资和消费随机最优控制问题的值函数所满足的线性抛物线偏微分方程和非线性抛物线偏微分方程.With the assumption of continuous-time model, this paper researches the optimal consumption and investment decision problem when the risky assets prices follow geometric Brown motion with stochastic volatility. Firstly the stochastic optimal control model for the optimal consumption and investment decision problem were established. Then the linear parabolic partial differential equation and the non-linearparabolic partial differential equation were obtained for the value function by using stochastic optimal control theory.

关 键 词：随机最优控制 最优投资模型 随机波动 

分 类 号：O232[理学—运筹学与控制论]