Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness
Optimization and Control
2025-05-21 v2 Mathematical Finance
Abstract
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.
Cite
@article{arxiv.2308.13850,
title = {Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness},
author = {Yunfei Peng and Wei Wei},
journal= {arXiv preprint arXiv:2308.13850},
year = {2025}
}
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32 pages