Mean field optimal stopping

Perelli Laura, Università degli Studi di Milano

We study a specific class of mean field optimal stopping problems by means of the dynamic pro- gramming approach. To do this we firstly focus on retrieving time-consistency through a suitable enlargement of the state space and a proper redefinition of the value function. Then we provide a dy- namic programming principle for the reformulated problem. Finally, using the notion of derivative with respect to a probability measure à la Lions, we derive the corresponding Hamilton-Jacobi- Bellman equation (which consists in a variational inequality in the 2nd order Wasserstein space) and we discuss existence and uniqueness results for its viscosity solutions.

Area: CS3 - Mean Field Games and Mean Field Control II (Andrea Cosso & Luciano Campi)

Keywords: mean field, optimal stopping, dynamic programming, Wasserstein space

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