Maximum principle for conditional mean-field FBSDEs systems with regime-switching involving impulse controls

Abstract

In this work, a stochastic control problem for a forward-backward regime-switching system with mean-field interactions involving impulse controls is studied. One feature of this study lies in the conditional mean-field term used in the model. Necessary conditions for both regular and impulse controls are established via convex variational technique, and the verification theorems are obtained under appropriate convexity assumptions as well. A mean-variance investment and consumption example is discussed to test the validity of the theoretical results, and numerical simulations are also carried out to make the results clearer.