On time-inconsistent stochastic control in continuous time

Time Inconsistent Stochastic Control in Continuous Time: Theory

In this paper, which is a continuation of the discrete time paper [4], we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled con...

Time-Inconsistent Stochastic Linear-Quadratic Control

Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

Stochastic Control in Continuous Time

A General Theory of Markovian Time Inconsistent Stochastic Control Problems

We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled Markov process and a fairly general objective functional we derive an ext...

Time-Inconsistent Discrete-Time Stochastic Linear-Quadratic Optimal Control: Time-consistent Solutions

In this paper, the time-consistent solutions of a timeinconsistent discrete-time stochastic linear-quadratic optimal control are investigated. Different from the existing literature, the definiteness constraint is not posed on the state and the control weight matrices of the cost functional. Necessary and sufficient conditions are, respectively, obtained to the existence of the open-loop time-c...