Optimal Consumption And Investment Portfolio Policy With Quadratic Utility Function

In 1970s, Merton established classical investment & consumption model. It was the pioneer of researching optimal investment and consumption problems, and has been the hot topic in the field of micofinance. People has a deep discussion about investment and consumption problems by using Stochastic dynastic planning theory,Stochastic control theory,Martingal and duality theory.The main task of this essay:First, under the condition of risk stocks satisfying geomatric Brownian,we give the optimal investment and consumption policy obeying a condition.Second, under the condition of the utility function of invester being quadratic fuction we get the demonstrastion solution of optimal investment & consume policy and wealth.