Abstract

In this paper, we study a class of mean-field singular stochastic optimal control problems for systems governed by regime-switching mean-field stochastic differential equations. The state dynamics depend on both regular and singular controls, and the coefficient of the singular component is allowed to depend explicitly on the state variable. We establish both necessary and sufficient stochastic maximum principles for this class of problems under the assumption that the control domain is convex. The presence of the state variable in the singular term leads to an adjoint process characterised by a generalised backward stochastic differential equation. As an application, we consider a one-dimensional regime-switching mean-field portfolio optimization problem with transaction costs, where the investor controls consumption and cumulative investment in a risky asset.

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