English

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.

Keywords

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}
}

Comments

32 pages

R2 v1 2026-06-28T12:05:00.492Z