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<p>This paper is concerned with a <i>discounted</i> stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the <i>asymptotic property</i> of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a dual method under certain convexity conditions of the Hamiltonian. As an application of our maximum principle, a linear quadratic production planning problem is solved with an <i>explicit</i> feedback optimal production rate. The existence and uniqueness of a <i>non-negative</i> solution to the associated algebraic Riccati equation are proved. Numerical experiments are reported to illustrate the theoretical results, especially, the <i>monotonicity</i> of the value function on various model parameters.</p>

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An Infinite Horizon Sufficient Stochastic Maximum Principle for Regime-Switching Diffusions and Applications

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Kai Ding,
  • Xun Li,
  • Siyu Lv,
  • Xin Zhang

摘要

This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a dual method under certain convexity conditions of the Hamiltonian. As an application of our maximum principle, a linear quadratic production planning problem is solved with an explicit feedback optimal production rate. The existence and uniqueness of a non-negative solution to the associated algebraic Riccati equation are proved. Numerical experiments are reported to illustrate the theoretical results, especially, the monotonicity of the value function on various model parameters.