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Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs (2310.11474v1)
Published 17 Oct 2023 in math.PR and math.OC
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.