Study on Optimal Consumption and Investment Tactics in Incomplete Market

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.