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本文研究风险溢价、不确定性和专利投资的多阶段性三者之间的关系,揭示投资决策理论的内在机理。利用最优控制模型给出了两阶段情况下的风险溢价的解析表达式,在多阶段的复杂情形下利用动态规划的数值迭代法给出了风险溢价的数值解。研究发现风险溢价在专利投资完成前后有很大差异,在专利投资完成后风险溢价仅随市场风险的增大而增大,但在专利投资完成前风险溢价不仅随着专利长度、已完成阶段数和未来的预期利润流的增大而降低、而且随着市场风险的增大而增大。这些结论是现有理论的创新和进一步完善,有利于在实践中做出更加合理的投资决策。
This paper studies the relationship between risk premium, uncertainty and multi-stage patent investment, revealing the inherent mechanism of investment decision theory. Using the optimal control model, the analytic expression of risk premium in two-stage case is given. The numerical solution of risk premium is given by using the numerical iteration method of dynamic programming under multi-stage and complex conditions. The research finds that the risk premium varies greatly before and after the completion of the patent investment. After the completion of the patent investment, the risk premium only increases with the increase of the market risk. However, before the completion of the patent investment, the risk premium not only varies with the length of the patent, And the expected future increase in profit flow and lower, but with the increase of market risk increases. These conclusions are the innovation and further improvement of the existing theories, which will help to make more rational investment decisions in practice.