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Mathematical mean-field approaches have been used in many fields, not only inPhysics and Chemistry, but also recently in Finance, Economics, and GameTheory. In this paper we will study a new special mean-field problem in apurely probabilistic method, to characterize its limit which is the solution ofmean-field backward stochastic differential equations (BSDEs) with reflections.On the other hand, we will prove that this type of reflected mean-field BSDEscan also be obtained as the limit equation of the mean-field BSDEs bypenalization method. Finally, we give the probabilistic interpretation of thenonlinear and nonlocal partial differential equations with the obstacles by thesolutions of reflected mean-field BSDEs.

Reflected Mean-Field Backward Stochastic Differential Equations. Approximation and Associated Nonlinear PDEs