Linear forward-backward stochastic differential equations with random coefficients
Abbreviated Journal Title
Probab. Theory Relat. Field
linear forward-backward stochastic differential equation; adapted; solution; decoupling reduction; Riccati backward stochastic differential; equation; CONTROL WEIGHT COSTS; RICCATI-EQUATIONS; QUADRATIC REGULATORS; CONSTRAINTS; Statistics & Probability
Solvability of linear forward-backward stochastic differential equations (FBSDEs, for short) with random coefficients is studied. A decoupling reduction method is introduced via which a large class of linear FBSDEs with random or deterministic time-varying coefficients is proved to be solvable. On the other hand, by means of Four Step Scheme, a Riccati backward stochastic equation (BSDE, for short) for (mxn) matrix-valued processes is derived. Global solvability of such Riccati BSDEs is discussed for some special (but nontrivial) cases, which leads to the solvability of the corresponding linear FBSDEs.
Probability Theory and Related Fields
"Linear forward-backward stochastic differential equations with random coefficients" (2006). Faculty Bibliography 2000s. 6741.