Forward-backward stochastic differential equations and their applications in finance

In this paper we present some results concerning the solvability of the adapted solutions to a class of forward-backward stochastic differential equations over an arbitrarily prescribed time duration, and several applications of such equations in mathematical finance. In particular, we introduce a direct scheme (called “four step scheme”) initiated by Ma-Protter-Yong (1994), which enables one to derive the explicit relations between the forward and backward components of the adapted solutions. Using the extensions of such a scheme in different directions, we then study some problems in finance including a console rate problem, a problem of hedging options for a large investor, and a stochastic Black-Scholes formula