Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations

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Subfields: Finance

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Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions (2021, methodology): “Such partial differential equations are also known as Master Bellman equations or Bellman equations in the Wasserstein space, see for instance [6, 14, 46].”
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).”
Splitting methods and short time existence for the master equations in mean field games (2020, methodology): “27 in [11]): |Upmq ́ Upm(1)q| ď d2pm,m(1)q sup μPP2 ˆ ˆ”
Superposition and mimicking theorems for conditional McKean–Vlasov equations (2020, background): “General results on existence, uniqueness, and limit theory require working with a notion of weak equilibrium which is well-suited for weak convergence arguments [18, 53, 17].”
Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity (2021, methodology): “[18, 30]) in mean field games with common noise.”