FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH MIXED INITIAL-TERMINAL CONDITIONS
Abbreviated Journal Title
Trans. Am. Math. Soc.
Forward-backward stochastic differential equations; mixed; initial-terminal conditions; Lyapunov operator; method of continuation; UTILITY; EXISTENCE; RISK; SDES; COEFFICIENTS; CONSUMPTION; UNIQUENESS; AMBIGUITY; FBSDES; AXIOMS; Mathematics
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.
Transactions of the American Mathematical Society
"FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH MIXED INITIAL-TERMINAL CONDITIONS" (2010). Faculty Bibliography 2010s. 991.