On the equilibrium strategy of linear-quadratic time-inconsistent control problems

Wei Ji; Wei Ji

doi:10.3934/math.2025253

AIMS Mathematics

2025, Volume 10, Issue 3: 5480-5494. doi: 10.3934/math.2025253

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Research article

On the equilibrium strategy of linear-quadratic time-inconsistent control problems

Wei Ji ^,

College of Science, Guiyang University, Guiyang 550005, China

Received: 08 October 2024 Revised: 11 February 2025 Accepted: 14 February 2025 Published: 11 March 2025
MSC : 49K15, 49N10, 91B50

The paper investigates the open-loop equilibrium strategy for linear-quadratic time-inconsistent control problems. It derives an equilibrium maximum principle for this strategy and establishes the equivalence among the open-loop equilibrium strategy, two-point boundary value problems, and the equilibrium Riccati equation. Additionally, examples are provided to illustrate the essential differences among the open-loop equilibrium strategy, the closed-loop equilibrium strategy, and the optimal control.
- equilibrium maximum principle,
- open-loop equilibrium strategy,
- time-inconsistent cost functional,
- linear-quadratic control problem
Citation: Wei Ji. On the equilibrium strategy of linear-quadratic time-inconsistent control problems[J]. AIMS Mathematics, 2025, 10(3): 5480-5494. doi: 10.3934/math.2025253

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Abstract

The paper investigates the open-loop equilibrium strategy for linear-quadratic time-inconsistent control problems. It derives an equilibrium maximum principle for this strategy and establishes the equivalence among the open-loop equilibrium strategy, two-point boundary value problems, and the equilibrium Riccati equation. Additionally, examples are provided to illustrate the essential differences among the open-loop equilibrium strategy, the closed-loop equilibrium strategy, and the optimal control.

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