The Application Of PDE In Stochastic Optimal Control

This paper illuminates stochastic optimal control problem based on the PDE, show Hamilton system, Hamilton function and Hamilton equation, and the optimal investment problem of pension by this method.Risk asset and non-risk one can be described by Winner process. Finance market also contains inflation and wage level. It could get optimal investment strategy by bringing in value function.Stochastic optimal control can be used widely, especially in finance investment. The investor can take into account charge and bonus in order to perfect the model. Because of the value function, it is hard to get the expression from the PDE of two ranks. How to use numerical method is also a problem.