@article{Ji2026, 
author = {Wei Ji and Yuanjiao Lei and Yinju Wei and Yandan Zhang},
title = {Open-loop equilibrium strategy of time-inconsistent deterministic linear-quadratic problems},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {4},
pages = {2419-2432},
keywords = {time-inconsistent, open-loop equilibrium, linear-quadratic, error function, two-point boundary value problem, Riccati-type equation},
url = {https://www.sciopen.com/article/10.3934/era.2026111},
doi = {10.3934/era.2026111},
abstract = {This paper investigates time-inconsistent linear-quadratic control problems within an open-loop framework, where the objective functional incorporates a non-exponential discounting structure. By introducing a two-point boundary value problem and a Riccati-type equation with an error function, it is established, under appropriate conditions, that the existence of an open-loop equilibrium strategy for the time-inconsistent control problem is equivalent to the existence of solutions to both the two-point boundary value problem and the Riccati-type equation. Furthermore, through an illustrative example, it is demonstrated that there exists an essential distinction between open-loop and closed-loop equilibria in time-inconsistent control problems.}
}