Optimal strategies of regular-singular mean-field delayed stochastic differential games

Abstract

In this paper, we investigate the mixed regular-singular control non-zero sum stochastic differential games problem under partial information where both the state dynamics and the performance functional contain time delay and mean field. We prove the existence and uniqueness of the solution of singular mean-field stochastic differential delayed equations and general reflected anticipated mean-field backward stochastic differential equations. By using Pontryagin’s maximum principle and Malliavin calculus, we establish sufficient maximum principles and necessary maximum principles about the non-zero sum game. Consequently, we find corresponding Nash equilibrium points and saddle points. Furthermore, we apply the results to study an optimal investment and dividend problem under model uncertainty.