信息的获取和数据的处理在当今金融市场扮演着重要的角色，数据分析有助于投资者理解信息，从而使其能够做出更好的预测，更好的了解因果关系，以及减少投资的不确定性。最终这些都可以帮助投资者做出更好的决策。然而，随之而来的数据分析的成本也会很自然的对投资者的最优决策产生不可忽略的影响。研究数据分析成本问题可以帮助我们理解和解释数据分析和一些经济行为的相互关联，同时这些问题的独特性也会对研究方法带来挑战，使我们需要对传统的随机优化控制理论，偏微分方程及倒向随机微分方程的数值算法进行改进，并且激发我们提出新方法以及相关的数学理论。本项目是第一个研究数据分析成本对投资者的最优决策，金融市场的均衡以及委托人－代理人问题的最优合同的影响。它将填补金融数学中对这些数据分析成本问题的研究的长期空白。另外，我们还会将最近具有突破性的的深度学习方法应用到上述问题的数值求解上。

The information acquisition and the date processing play important roles in today's financial markets. Data analytics can enable investors to make better forecasts, to have better understanding on causal relationships and to reduce uncertainty to some extent, all of which lead to better decision making. However, the cost of data analytics also inevitably has non-negligible impacts on the investors’ optimal decisions, which has been ignored for a long time. Studying such problems with data analytics cost therefore can allow us to understand and explain the relationship between data analytics and some economic behaviors. At the same time, these novel problems will bring new challenges to the research methods. They will require us to improve the traditional stochastic optimal control theory and the numerical methods for PDEs and BSDEs, and also inspire us to suggest new methods and new mathematical theory. This project is the first one that focuses on the impact of data analytics on the investors’ optimal decisions, the financial market equilibrium, and the optimal contract in the Principal-Agent problem. It will fill the long-term gaps in the study of problems related to the cost of data analytics in financial mathematics. In addition, we will also apply the recent breakthrough deep learning methods to find numerical solutions for the above problems.