Abstract: In this paper,we analyze the relation among risk premium,uncertainty and multi-stages of patent investment,in order to reveal the internal mechanism of investment decision theory.Using the optimal control model,we firstly derive the analytic expression of risk premium in the situation of two-stage. Under more than two stages case,numerical solution is presented by using numerical iteration algorithm based on dynamic programming.It is shown that the risk premium has significant differences between the pre-and post patent investment completion.After completion patent investment,the risk premiumonly increases with the increasing market risk.On the other hand,before completion with the increasing market risk,the risk premium increases accordingly,but the result turns out contrary to that of increasing patent length,the number of completed stages and expected future cash flow.Our results will help to bring forth new ideas on the extant theory,and to make a scientific investment decisions.

Key words: risk premium, uncertainty, patent length, market risk, real options, investment decisions