Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs

Understand

This work concerns the optimal control problem for McKean-Vlasov SDEs.

• In order to characterize the value function, we develop the viscosity solution theory for Hamilton-Jacobi-Bellman (HJB) equations on the Wasserstein space using Mortensen's derivative.
• In particular, a comparison principle for viscosity solution is established.
• Our approach is based on Borwein-Preiss variational principle to overcome the loss of compactness for bounded sets in the Wasserstein space.