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Abstract

Classical optimal control problems for (ordinary, stochastic, or evolutionary partial) differential equations have the following feature: When an optimal control is found for a given initial time and initial state, the optimal control will remain optimal as time goes by along the optimal trajectory. This is called the time-consistency of the problem. However, in reality, more than often, the optimal control will hardly stay optimal later on. This is called the time-inconsistency. This mainly is due to the time-preferences and risk-preferences of the decision-makers involved. When the problem is time-inconsistent, one should try to find locally optimal, time-consistent equilibrium strategies. In this talk, we will survey the results that we have obtained in the past decay.