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On the Time-Inconsistent Deterministic Linear-Quadratic Control

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arxiv 2105.03670 v3 pith:T4MP6HWI submitted 2021-05-08 q-fin.MF

Hongyan Cai , Danhong Chen , Yunfei Peng , Wei Wei This is my paper · ORCID
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keywords controldeterministictime-inconsistentlinear-quadraticproblemproblemsriccatiarises
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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.

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