Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints

Abstract

In this paper, we study the reflected stochastic differential equations driven by G-Brownian motion (reflected G-SDEs) with two nonlinear constraints. With the help of the Skorokhod problem with nonlinear constraints, we first study the doubly reflected G-Brownian motion, which is constructed pathwise and lies in the same G-expectation space as the G-Brownian motion. For the reflected G-SDE, the uniqueness is derived from some a priori estimate and the existence is obtained by a Picard iteration method. The comparison theorem of the solution and the individual constraining processes are provided.