Existence of optimal feedback controls for McKean-Vlasov SDEs

This work concerns the optimal control problem for McKean-Vlasov SDEs. We provide explicit conditions to ensure the existence of optimal Markovian feedback controls. Moreover, based on the flow property of the McKean-Vlasov SDE, the dynamic programming principle is established, which will enable to characterize the value function via the theory of Hamilton-Jacobi-Bellman equation on the Wasserstein space.