Forward-backward stochastic differential equations driven by G-Brownian motion under weakly coupling condition

Abstract

In this paper, we obtain the existence and uniqueness theorem of $L^p$-solution for coupled forward-backward stochastic differential equations driven by G-Brownian motion (G-FBSDEs) with arbitrary $T$ under weakly coupling condition. Specially, the result for $p\in (1,2)$ is completely different from the one for $p\ge 2$. Furthermore, by considering the dual linear FBSDE under a suitable reference probability, we establish the comparison theorem for G-FBSDEs under weakly coupling condition.

19 pages