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arXiv · 2509.14495

A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon

Qingmeng Wei·Jiongmin Yong
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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.

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Qingmeng Wei, Jiongmin Yong. 2025-09-18. A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon. https://arxiv.org/abs/2509.14495

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