  This paper is concerned with a kind of risk-sensitive optimal control problem
for fully coupled forward-backward stochastic systems. The control variable
enters the diffusion term of the state equation and the control domain is not
necessarily convex. A new global maximum principle is obtained without assuming
that the value function is smooth. The maximum condition, the first- and
second-order adjoint equations heavily depend on the risk-sensitive parameter.
An optimal control problem with a fully coupled linear forward-backward
stochastic system and an exponential-quadratic cost functional is discussed.
The optimal feedback control and optimal cost are obtained by using Girsanov's
theorem and completion-of-squares approach via risk-sensitive Riccati
equations. A local solvability result of coupled risk-sensitive Riccati
equations is given by Picard-Lindel$\ddot{o}$f's Theorem.
