An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications

TL;DR

This paper develops a maximum principle for infinite horizon regime switching diffusions, providing theoretical insights and practical solutions for stochastic control problems with applications in production planning.

Contribution

It introduces a new sufficient stochastic maximum principle for infinite horizon regime switching diffusions and applies it to solve a linear quadratic control problem.

Findings

Established well-posedness of infinite horizon stochastic differential equations.

Derived explicit feedback control for a production planning problem.

Numerical experiments confirm theoretical properties like value function monotonicity.

Abstract

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.