Title：A forward dynamic approach for some time inconsistent problems
Speaker：Prof. Jianfeng Zhang, University of Southern California
Time inconsistency means that an optimal control obtained today becomes non-optimal anymore tomorrow. This kind of phenomena appears often in practice, and it has been a major subject in economics. In recent years it has also received strong attention in mathematics community, both for its practical importance and for its mathematical challenge. The main challenge is that many tools for time consistent problems, for example PDEs and comparison principles, fail in these settings. There are typically two approaches, one is the equilibrium approach which can be viewed as a backward approach. In this approach the problem is reformulated as a game problem where the player plays with infinitely many future selves. We shall propose a forward approach, motivated by the so called forward utility. We remark that the two approaches lead to different value functions and thus are different math problems. In this talk we will explain the two approaches and motivate the forward approach.