Backward stochastic differential equations driven by -Brownian motion

In this paper, we study the backward stochastic differential equations driven by a G -Brownian motion ( B t ) t ≥ 0 in the following form: Y t = ξ + ∫ t T f ( s , Y s , Z s ) d s + ∫ t T g ( s , Y s , Z s ) d 〈 B 〉 s − ∫ t T Z s d B s − ( K T − K t ) , where K is a decreasing G -martingale. Under Lipschitz conditions of f and g in Y and Z , the existence and uniqueness of the solution ( Y , Z , K ) of the above BSDE in the G -framework is proved.