Financial And Investment Decision-making Model

This paper utilizes stochastic optimal control theory, Ito formula in stochastic analysis and nonlinear filter technique to maximize the expected utility from the terminal wealth. Firstly, the paper provides a simple review to some problems on investment and consumption. Secondly, the paper derives HJB equation by means of It: formula and nonlinear filter technique, and obtains some necessary conditions of the optimal strategy. Furthermore, the paper puts forward a successful trial solution to solve the partial differential equation for that necessary conditions. By utilizing this trial solution, the paper obtains the optimal strategy for the power utility under full information. Especially, the paper provides the optimal solution for logarithmic utility under both lull and partial information, by utilizing Ito formula only. By comparing optimal target function, the paper shows a concise formula to the valuation of information. In the end, assuming the borrowing rate is bigger than saving rate , the paper provides explicit solutions to both logarithmic utility with partial information and power utility with full information by Ito's formula other than the complicated dynamic programming. All of the strategies are suitable for operating online.