Quantitative Stability and Contraction Principles for Mean-Field G-SDEs
Abstract
We study mean-field stochastic differential equations (SDEs) driven by G-Brownian motion, extending recent work on existence and uniqueness by developing a full quantitative stability framework. Our main contribution is the construction of an intrinsic stability modulus that provides explicit bounds on the sensitivity of solutions with respect to perturbations in initial data (and, indirectly, coefficients). Using Bihari-Osgood type inequalities under G-expectation, we establish sharp continuity estimates for the data-to-solution map and analyze the asymptotic properties of the stability modulus. In particular, we identify contraction behavior on short horizons, leading to a contraction principle that guarantees uniqueness and global propagation of stability. The results apply under non-Lipschitz, non-deterministic coefficients with square-integrable initial data, thereby significantly broadening the scope of mean-field G-SDEs. Beyond existence and uniqueness, our framework quantifies robustness of solutions under volatility uncertainty, opening new directions for applications in stochastic control, risk management, and mean-field models under ambiguity.