  An indefinite stochastic Riccati Equation is a matrix-valued, highly
nonlinear backward stochastic differential equation together with an algebraic,
matrix positive definiteness constraint. We introduce a new approach to solve a
class of such equations (including the existence of solutions) driven by
one-dimensional Brownian motion. The idea is to replace the original equation
by a system of BSDEs (without involving any algebraic constraint) whose
existence of solutions automatically enforces the original algebraic constraint
to be satisfied.
