Optimal control models with random switches and applications to economics and management

This survey examines the role of stochastic switching times in optimal control theory with a particular emphasis on applications in economics and management. We start with a review of the problem’s formulation and early foundational contributions, followed by an outline of the general model framework. We highlight the structural key components and illustrate the sequence of decision stages. Two main methodological approaches are explored: a backward solution technique and an age-structured (vintage) optimal control formulation. We analyze how both approaches inform the determination and characterization of switching times in the dynamic optimization nexus. The survey further illustrates the relevance of random switching dynamics by applications in environmental economics, health economics and other related domains. Finally, we discuss current challenges and avenues for future research, including the incorporation of multiple switching events, agent heterogeneity, and the consideration of smaller shocks that occur frequently, almost continuously. This synthesis aims to provide both a rigorous theoretical perspective and a practical applied viewpoint on switching times–as critical components of decision-making in economics, finance, management and the broader social sciences–by leveraging mathematical modelling, analytical methods and computational techniques.