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

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arxiv 2310.11474 v1 pith:YYRPB2DT submitted 2023-10-17 math.PR math.OC

Jinghai Shao This is my paper · ORCID
classification math.PRmath.OC
keywords viscositycontrolequationsmckean-vlasovoptimalprincipleproblemsdes
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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.

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