In Liang et al (2009), the current authors demonstrated that BSDEs can be
reformulated as functional differential equations, and as an application, they
solved BSDEs on general filtered probability spaces. In this paper the authors
continue the study of functional differential equations and demonstrate how
such approach can be used to solve FBSDEs. By this approach the equations can
be solved in one direction altogether rather than in a forward and backward
way. The solutions of FBSDEs are then employed to construct the weak solutions
to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a
nonlinear version of Girsanov's transformation. As the solving procedure is
constructive, the authors not only obtain the existence and uniqueness theorem,
but also really work out the solutions to such class of BSDE systems with
quadratic growth. Finally an optimal portfolio problem in incomplete markets is
solved based on the functional differential equation approach and the nonlinear
Girsanov's transformation.Comment: 26 page
