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arXiv · 2310.11474

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

Jinghai Shao
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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.

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Jinghai Shao. 2023-10-17. Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs. https://arxiv.org/abs/2310.11474

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