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<p>In this paper, we focus on the approximate maximum principle for discrete-time stochastic optimal control problems with a non-convex control domain. We consider a sequence of discrete-time stochastic control systems that can approximate a continuous-time stochastic control system. We provide the convergence results for optimal control and the cost functional, and based on this, we obtain the convergence of the state process and the adjoint processes. As an application of these results, we develop a discrete-time approximation method to prove the classical general maximum principle, thereby establishing the connection between the approximate maximum principle and the general maximum principle.</p>

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Discrete-time approximate stochastic maximum principle

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Bozhang Dong,
  • Tianyang Nie,
  • Zhen Wu

摘要

In this paper, we focus on the approximate maximum principle for discrete-time stochastic optimal control problems with a non-convex control domain. We consider a sequence of discrete-time stochastic control systems that can approximate a continuous-time stochastic control system. We provide the convergence results for optimal control and the cost functional, and based on this, we obtain the convergence of the state process and the adjoint processes. As an application of these results, we develop a discrete-time approximation method to prove the classical general maximum principle, thereby establishing the connection between the approximate maximum principle and the general maximum principle.