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Extended Mean Field Control Problems: Stochastic Maximum Principle and Transport Perspective

2019; Society for Industrial and Applied Mathematics; Volume: 57; Issue: 6 Linguagem: Inglês

10.1137/18m1196479

1095-7138

Beatrice Acciaio, Julio Backhoff‐Veraguas, René Carmona,

Markov Chains and Monte Carlo Methods

We study mean field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufficient forms, which extend the known conditions to this general framework. We suggest a variational approach for a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme.