A stochastic maximum principle for singular mean-field regime-switching optimal control

TL;DR

This paper develops a maximum principle for optimal control problems involving mean-field regime-switching stochastic differential equations with singular controls, providing theoretical tools for complex financial models.

Contribution

It introduces necessary and sufficient maximum principles for singular mean-field regime-switching control problems, including non-convex control domains and second-order adjoint processes.

Findings

Derived maximum principles for singular mean-field regime-switching systems.

Applied theoretical results to an inter-bank borrowing and lending model.

Extended control theory to non-convex domains with regime dependence.

Abstract

In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular and a singular control, and the coefficient associated with the singular component is allowed to be regime dependent. We derive both necessary and sufficient singular stochastic maximum principles. Because the regular control domain is not assumed to be convex, we employ the spike variation technique and obtain the necessary maximum principle by introducing a second-order adjoint process. As an application, we use the main theoretical results to analyse an inter-bank borrowing and lending model with transaction costs.