Time inconsistency and self-control optimization problems: Progress and challenges

Time inconsistency has been an important issue in many stochastic decision problems arisen in real life and financial decision making, especially in the dynamic investment area. When a stochastic decision problem is time inconsistent, the decision maker would be puzzled by his/her conflicting decisions “optimally” derived from his/her time-varying preferences at different time instants. In the literature, the time inconsistent problem is also called the self-control problem, as the decision maker needs to exert proper self-control to resist present temptation and then achieve a better long-term performance. Different approaches dealing with time inconsistency in the literature are reviewed in this paper. After that, the open questions and challenges are also discussed.