Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games

By René A. Carmona, François Delarue. 2018

572 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/fe441f837c19029c838ef91f1c85dd89a12a8857

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Citations in the corpus

Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, background): “In addition, Carmona– Delarue [9,10] and Carmona–Delarue–Lachapelle [11] developed probabilistic theory of mean-field including mean-field forward–backward stochastic differential equations (MF-FBSDEs, for short), control and games.”
Mean–field moral hazard for optimal energy demand response management (2019, methodology): “Nevertheless, it has been proved in Carmona and Delarue (2018) that particles become asymptotically independent conditionally on the common noise, and that the empirical distribution converges toward the common conditional distribution of each particle given the common noise (𝜇 in our case).”
McKean–Vlasov optimal control: The dynamic programming principle (2019, unknown): “[25]).”
Necessary Optimality Conditions for Optimal Control Problems in Wasserstein Spaces (2021, background): “[9,11,15,42] and [17,37] in connection with the theory ofmean-field games.”
Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence (2020, background): “We refer to [16, 19, 34, 35] and the references therein for some of the recent results.”
Weak quantitative propagation of chaos via differential calculus on the space of measures (2019, result): “2 of [9], Φ(m)(t, ·) is differentiable in measure with its derivative given by ∂μΦ (t, μ)(y) = ∂xp(y, μ) + ∫”