Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system

2025/09/11 by Xun Li, Fan Wu, Li, Xun +3 · 2 citations
Computer Science · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Stability and Control of Uncertain Systems #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2509.09358

openalex publication_date 2025/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the long-time behavior of zero-sum stochastic linear-quadratic (SLQ) differential games within Markov regime-switching diffusion systems and establishes the turnpike property of the optimal triple. By verifying the convergence of the associated coupled differential Riccati equations (CDREs) along with their convergence rate, we show that, for a sufficiently large time horizon, the equilibrium strategy in the finite-horizon problem can be closely approximated by that of the infinite-horizon problem. Furthermore, this study enhances and extends existing results concerning zero-sum SLQ differential games over both finite and infinite horizons.

Citations

• Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
• Open-loop and closed-loop solvabilities for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
• Stochastic linear-quadratic differential game with Markovian jumps in an infinite horizon
• Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games
• Stochastic linear quadratic optimal control problems with regime-switching jumps in infinite horizon
• The exponential turnpike property for periodic linear quadratic optimal control problems in infinite dimension
• Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control
• Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems
• Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems
• Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Games
• The turnpike property in nonlinear optimal control -- A geometric approach
• On the Turnpike Property and the Receding-Horizon Method for\n Linear-Quadratic Optimal Control Problems
• Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points
• A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls
• A Mathematical Theory of Saving

Cited by

• Turnpike Property of Mean-Field Linear-Quadratic Optimal Control Problems in Infinite-Horizon with Regime Switching
• System-Theoretic Analysis of Dynamic Generalized Nash Equilibrium Problems -- Turnpikes and Dissipativity

Related

• Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games
• Open-loop and closed-loop solvabilities for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
• Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
• Turnpike properties in linear quadratic Gaussian N-player differential games
• Zero-sum stochastic linear-quadratic Stackelberg differential games of Markovian regime-switching system