非完全市场最优消费和投资策略研究

Study on Optimal Consumption and Investment Tactics in Incomplete Market

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方差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 ,最后与经典 Merton问题进行了比较。

Under the assumption continuous-time model,this paper researches the optimal consumption and investment decision problem when the risk assets prices follow geometric Brownian motion with stochastic volatility. First,the stochastic optimal control models for the optimal consumption and investment decision problem was established. Then the partial differential equation was obtained for the value function by using stochastic optimal control theory. At last the paper makes a comparative analysis on a classical Merton problem.