What question did this study set out to answer?

This work aims to establish unique viscosity solutions for fully second-order Hamilton–Jacobi–Bellman equations in mean field control contexts.

Viscosity Solutions of Fully Second-Order HJB Equations in the Wasserstein Space

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Randomized trial shows unique viscosity solutions for mean field control problems, suggesting new frameworks for analysis.

This work aims to establish unique viscosity solutions for fully second-order Hamilton–Jacobi–Bellman equations in mean field control contexts.
Utilizes smooth approximations from particle systems as outlined by Cosso et al.
Applies a compactness argument using measure moment penalization as indicated by Soner and Yan.
Explores dynamics influenced by state-dependent common noise volatility.
Establishes that the value functions in mean field control problems are unique viscosity solutions.
Demonstrates the flexibility in dealing with infinite-dimensional state-dependent derivatives.
Presents the first results addressing unbounded dynamics in this context.

Bayraktar et al. (2026) studied this question.

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