  A general backward stochastic linear-quadratic optimal control problem is
studied, in which both the state equation and the cost functional contain the
nonhomogeneous terms. The main feature of the problem is that the weighting
matrices in the cost functional are allowed to be indefinite and cross-product
terms in the control and the state processes are present. Necessary and
sufficient conditions for the solvability of the problem are obtained, and a
characterization of the optimal control in terms of forward-backward stochastic
differential equations is derived. By a Riccati equation approach, a general
procedure for constructing optimal controls is developed and the value function
is obtained explicitly.
