arXiv Analytics

Sign in

arXiv:2310.11474 [math.PR]AbstractReferencesReviewsResources

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

Jinghai Shao

Published 2023-10-17Version 1

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.

Comments: 28 pages. arXiv admin note: text overlap with arXiv:2310.10950
Categories: math.PR, math.OC
Subjects: 60H10, 35Q93, 49L25
Related articles: Most relevant | Search more
arXiv:2309.08080 [math.PR] (Published 2023-09-15)
Optimal control problem for reflected McKean-Vlasov SDEs
arXiv:2310.15854 [math.PR] (Published 2023-10-24)
Control of McKean--Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity
arXiv:2203.17162 [math.PR] (Published 2022-03-31)
Viscosity solutions for obstacle problems on Wasserstein space

Links

Toolbox