Master Bellman equation in the Wasserstein space: uniqueness of viscosity solutions

Rosestolato Mauro, Università di Genova

In this talk we address the Master Bellman equation in the Wasserstein space arising in the study of mean field control problems, and we aim to provide the main ideas underlying a comparison result for viscosity solutions. Since classical arguments do not apply to the present framework, due to the awkward nature of the underlying Wasserstein space, an alternative stragety is presented, relying on two key features. First, a finite-dimensional approximation of the value function is obtained in terms of the relative n-player game. Secondly, a smooth gauge-type function is used to generate maxima/minima through an extension of the Borwein-Press generalization of Ekeland's variational principle.

Area: IS7 - Stochastic optimal control of McKean-Vlasov equations (Elena Bandini)

Keywords: Master Bellman equation, Viscosity solutions

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