2025/06/13 by Ding, Kai, Li, Xun, Lv, Siyu +1
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2506.11523
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 condition 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.