Abstract
We investigate coupled forward backward stochastic differential equations driven by the G-Brownian motion (Bt)t≥0 which take the form,(0.1)Xt=x+∫0tb(s,Xs,Ys)ds+∫0tσ(s,Xs,Ys)dBsYt=ψ(XT)+∫tTg(s,Xs,Ys,Zs)ds−∫tTZsdBs−(KT−Kt), where K being part of the solution, is required to be some decreasing G-martingale. Under the Lipschitz assumptions, the existence and uniqueness of the solution (X,Y,Z,K) in small time duration is proved by using the contraction mapping principle. Different from the classical case, the integrability orders for components X,Y,Z,K of solutions are not homogeneous, which is the main characteristic for this problem under the G-expectation framework.
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