On Singular Control Problems with State Constraints and Regime-Switching: A Viscosity Solution Approach

Abstract

This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the singular control. Such a formulation stems from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in random environments. With the aid of weak dynamic programming principle and an exponential transformation, we characterize the value function to be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi-variational inequalities. Several examples are analyzed in details to demonstrate the main results.

References in corpus (2)

• Singular control with state constraints on unbounded domain
• HJB equations for certain singularly controlled diffusions

Cited by in corpus (4)

• The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking
• The existence of optimal control for continuous-time Markov decision processes in random environments
• The existence of optimal feedback controls for stochastic dynamical systems with regime-switching
• Optimal Control of Markov Regime-Switching Stochastic Recursive Utilities