Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs
arXiv:2310.11474
Abstract
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.
28 pages. arXiv admin note: text overlap with arXiv:2310.10950