时间不一致随机控制理论及其应用

从2004年基德兰德和普雷科斯特关于“时间一致性”理论的研究获得诺贝尔经济学奖后，“时间一致性”问题已成为经济学及控制论等领域的研究热点。“随机”因素对经济活动的干扰，使得“随机”的“时间不一致”问题有待深入研究。本项目以随机控制理论为基础，以倒向随机微分方程理论为核心，深入研究时间不一致的随机控制问题及其在经济金融中的应用。重点对时间不一致的递归效用随机控制问题及线性二次控制问题进行研究，将所得理论应用到实际的时间不一致问题，加强与国内外经济金融领域合作，得到一批领先的基础及应用成果。希望通过本项目的研究，为政策的制定者、经济活动的参与者提供有力的理论指导和应用工具，保证制定的策略，实施效果不会因为时间的影响而发生“变化”。

The theory of “time consistency” has been a hot research topic in economic and control fields since the research about time consistency of Finn E. Kydland and Edward C. Prescott wined the Nobel Economic Prize in 2004. But the effects of “random” on the economic activities make the time-inconsistent stochastic problem need to be deeply studied. Based on the stochastic control theory, the project will study time-inconsistent stochastic control problem and the related applications in economics and finance. We will focus on the following themes: time-inconsistent recursive stochastic control problem and time-inconsistent linear quadratic control problem. Finally, we will apply the results to the time-inconsistent problems in reality. And we will strengthen the cooperation with financial departments to get a batch of the forefront theoretical and application results in the field of financial mathematics. We hope our research can help the decision-makers to get the nice policies, which will keep the same effects as time goes by.