Robust McKean--Vlasov Variational Systems with Asymmetric Loss Aversion: Well-Posedness, Stability, and Propagation of Chaos for the Forward and Regularized Backward Systems

Abstract

We study a class of robust forward--backward McKean--Vlasov variational systems under model uncertainty represented by a non-dominated family of probability measures. Mean-field interactions are described through nonlinear collective observables acting on the laws of the forward and backward components. To model asymmetric loss aversion, we introduce a nonsmooth convex functional whose subdifferential defines a law-dependent maximal monotone operator acting on the forward state. We establish existence, uniqueness, and stability of the robust forward dynamics by a fixed-point argument in Wasserstein space. The backward component is formulated as a selected backward variational system rather than a classical backward stochastic variational inequality. Our analysis relies on Yosida regularization, uniform a priori estimates, convergence of the regularized solutions, and a Minty--Brézis identification argument, yielding a canonical solution associated with the minimal norm selection. We further construct a particle approximation and prove propagation of chaos for the forward dynamics with explicit convergence rates uniformly over the non-dominated family. For each fixed regularization parameter, we also establish quantitative propagation of chaos for the regularized backward component and explain why estimates uniform in both the number of particles and the regularization parameter require additional non-contact assumptions near the nonsmooth threshold.