Stochastic Differential Equations Driven by G-Brownian Motion with Mean Reflections

Abstract

In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first investigating the Skorokhod problem with mean reflection under G-expectation. Two approaches to constructing the solution are introduced, both offering insights into desired properties and aiding in the application of the contraction mapping method.