Finding adapted solutions of forward–backward stochastic differential equations: method of continuation

Summary. The notion of bridge is introduced for systems of coupled forward–backward stochastic differential equations (FBSDEs, for short). This notion helps us to unify the method of continuation in finding adapted solutions to such FBSDEs over any finite time durations. It is proved that if two FBSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBSDEs. Received: 23 April 1996 / In revised form: 10 October 1996