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

2025/09/18 by Wei, Qingmeng, Yong, Jiongmin
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2509.14495

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.

Citations

• Time-inconsistent Linear Quadratic Optimal Control Problem for Forward-Backward Stochastic Differential Equations
• Nonlocal Fully Nonlinear Parabolic Differential Equations Arising in Time-Inconsistent Problems
• Time-Inconsistent Recursive Stochastic Optimal Control Problems
• Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions
• Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
• Time-Inconsistent Stochastic Linear--Quadratic Control
• Myopia and Inconsistency in Dynamic Utility Maximization

Related

• Time Inconsistent Stochastic Control in Continuous Time: Theory and Examples
• Time-Inconsistent Stochastic Optimal Control Problems and Backward Stochastic Volterra Integral Equations
• Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
• Time-Inconsistent Recursive Stochastic Optimal Control Problems
• The Maximum Principle in Time-Inconsistent LQ Optimal Control Problem for Jump Diffusions