A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon
Optimization and Control
2025-09-19 v1
Abstract
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time. Under such a condition, the problem in an infinite time horizon can be decomposed into two parts: a non-autonomous time-consistent problem in an infinite time horizon and a time-inconsistent problem in a finite time horizon. Then an equilibrium strategy will be constructed. Both Bolza type problem and recursive cost problem are considered.
Cite
@article{arxiv.2509.14495,
title = {A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon},
author = {Qingmeng Wei and Jiongmin Yong},
journal= {arXiv preprint arXiv:2509.14495},
year = {2025}
}