Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents

Understand

We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent.

• Their distinguishing feature is that the classical Bellman optimality principle no longer holds.
• Our formulation is cast within the framework of a controlled non-Markovian forward stochastic differential equation, and a general objective functional setting.
• We adopt a game-theoretic approach to study such problems, meaning that we seek for sub-game perfect Nash equilibrium points.