Forward-backward stochastic differential equations with mixed initial-terminal conditions

Abstract:

Well-posedness of forward-backward stochastic differential equations (FBSDEs, for short) in $L^p$ spaces with mixed initial-terminal conditions is studied. A notion of Lyapunov operator is introduced, whose existence leads to a priori estimates of the adapted solutions sufficient for the well-posedness of the corresponding FBSDEs, via the method of continuation. Various situations are discussed under which Lyapunov operators do exist.