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Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness

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arxiv 2308.13850 v2 pith:YSRVA7TL submitted 2023-08-26 math.OC q-fin.MF

Yunfei Peng , Wei Wei This is my paper · ORCID
classification math.OCq-fin.MF
keywords equationssolutionsuniquenessclasscontroldeterministicequilibriumlinear
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In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from non-exponential discount functions. We characterize the solutions to the HJB equations using a class of Riccati equations with integral terms. By studying the uniqueness of solutions to the integro-differential Riccati equations, we prove the uniqueness of solutions to the equilibrium HJB equations.

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