On the Time-Inconsistent Deterministic Linear-Quadratic Control

Hongyan Cai, Danhong Chen, Yunfei Peng and Wei Wei

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Abstract: A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general time-inconsistent deterministic LQ problem, where the inconsistency arises from non-exponential discount functions. By studying the solvability of the Riccati equation, we show the existence and uniqueness of the linear equilibrium for the time-inconsistent LQ problem.

Date: 2021-05, Revised 2021-10
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