本项目旨在以随机分析中的(正)倒向随机微分方程理论为基础，深入研究一般情形下的平均场(正)倒向随机微分方程(即，此时方程的系数依赖于解以及解引出的分布)，及其在随机控制、随机微分对策、偏微分方程、金融等方面的应用，具体来说: 1.利用一般情形下的平均场(正)倒向随机微分方程研究新型的定义在概率集合上的非局部偏微分方程(包括相应的Hamilton-Jacobi-Bellman(-Isaacs)方程)的粘性解的存在唯一性；2.研究一般情形下的平均场(正)倒向随机微分方程在各种非Lipschitz条件下的解的存在性以及比较定理；3.研究(非扩张条件下)随机微分对策问题以及平均场情形下的随机控制问题中的Abel均值和Cesaro均值的极限的表示定理等。得到一批在相关领域居于国际前沿的成果。

For the future works the applicant will continue the study on the theory of general mean field (forward) backward stochastic differential equations (SDEs) (i.e., the coefficients depend not only on the solution but also the law induced by the solution), and its applications in stochastic control, stochastic differential game, partial differential equations and mathematical finance. A particular attention among these future works will be paid to challenging problems in the interface between classical stochastic control and game theory on one hand and, on the other hand, the modelization of mean field interaction (a very recent research topic motivated by a large number of involved agents or players). Related subjects include: 1. The study of viscosity solutions of non-linear partial differential equations (PDEs) over spaces of probability measures-a completely new type of PDEs (including HJB equations and HJB-Isaacs equations)-with the help of general (forward) backward SDEs of mean field type; 2. The existence of the solution and the comparison theorems of general (forward) backward SDEs of mean field type under non-Lipschitz conditions; 3. Representation of limit values of Abel mean and Cesaro mean for nonexpansive stochastic differential games and also nonexpansive stochastic differential control in the mean field case. . The applicant has achieved different research results of high international level in the fields of stochastic differential games, forward-backward stochastic differential equations, stochastic control, and mathematical finance. 33 SCI papers were published including 20 SCI papers during the recent five years. Our papers have been cited 272 times by SCI papers of other authors between 2013 and 2017. Our papers until now have been commented, generalized and cited by a lot of international famous experts, among them, the famous French academicians Professors P.L. Lions (who is also the winner of Fields Prize) and A. Bensoussan (who is also one of the founders of the modern stochastic control theory and former chief of the French Space Research Center); the outstanding American mathematicians Professors W.H. Fleming and N.V. Krylov. The applicant has got the Excellent Youth Fund of National Natural Science, the fund from the program for New Century Excellent Talents in University, the Distinguished Youth Fund of Natural Science of Shandong Province, as well as a Newton Advanced Fellowship.