Optimal Consumption and Investment Decision Problem with Stochastic Volatility

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.