  In this paper, we solve an optimal control problem governed by a system of
mean-field stochastic differential equations with multiple defaults (MMFSDEs).
We transform the global optimal control problem into several optimal control
subproblems governed by a system of mean-field stochastic differential
equations with single default (SMFSDEs) and derive both the sufficient and
necessary maximum principles for these subproblems. We also give the existence
and uniqueness of solutions to the MMFSDEs and the mean-field backward
stochastic differential equations with multiple defaults (MMFBSDEs),
respectively. Finally, as an example, our results are applied to obtain the
explicit solution for an optimal control problem whose cost function is
considered as a recursive utility process with multiple defaults.
