  A linear quadratic optimal stochastic control problem with random
coefficients and indefinite state/control weight costs is usually linked to an
indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic
backward stochastic differential equation along with an algebraic constraint
involving the unknown. Either the optimal control problem or the SRE is
solvable only if the given data satisfy a certain structure condition that has
yet to be precisely defined. In this paper, by introducing a notion of
subsolution for the SRE, we derive several novel sufficient conditions for the
existence and uniqueness of the solution to the SRE and for the solvability of
the associated optimal stochastic control problem.
