Viscosity Solutions of Fully Second-Order HJB Equations on Wasserstein Space
A well-posedness result showing that value functions of mean field control problems with common noise are the unique viscosity solutions, in a Crandall-Lions-style framework, of Hamilton-Jacobi-Bellman equations on the Wasserstein space whose second-order derivative in the measure variable is state-dependent and genuinely infinite-dimensional. Existence uses smooth approximations built from finite particle systems; uniqueness rests on a comparison theorem obtained via compactness from penalization of measure moments, and the setting allows unbounded dynamics and state-dependent common-noise volatility.
Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space∗ Erhan
In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman equations, in a Crand…