Consider the minimization of the following quadratic cost functional: J (u):=E<Mx/T, x/T>+E ∫T (<QsTs, xs>+<Nsus, us>) ds, where x is the solution of the following linear stochastic control system: dxt=(Atxt+btut)dt +∑d (cixt+diut) dWi, u is a square integrable adapted proce;s. The problem :s convenally called the stochastic LQ (the abbreviation of "linear quadratic") problem. We are concerned with the following general case: the coefficients A, B, Ci, Di, Q, N, and M are allowed to be adapted processes or random matrices or random matrices We prove the existence and uniqueness result for the associated Riccati equation, which in our general case is a backward stochaatic differential equation with the generator (the drift term) being highly nonlinear in the two unknown variables. This solves solves Bismut and Peng's long-standing open problem (for the case of a Brownian filtration), which was initially proposed by the French mathemation J. M. Bismut [in Seminaire de Probabilites XII, Lecture Notes in Math. 649. C. Dellacherie, P. A. Meyer, and M. Weil, eds., Springer-Verlag, Berlin, 1978, pp. 180-264]. We also provide a rigorous derivation of the Riccati equation from the stochastic Hamilton system. This completes the interrellationship between the Riccati equation and the stochastic Hamilton system as two different but equivalent tools for the stochastic LQ problem. There are, two key points in our argumentsl. The first one is to connect the existence of the solution of the Riccati equation to the homomorphism of the stochastic flows derived form theoptimally contrrolled system. Actually, we establish their equivalence. As a consequence, we canconstruct solutions to a sequence of suitably modified Riccati equations in terms of the associated stochasic Hamilton systems (and the optimal controls). The soco:nd koy point is to establish a new type of a priori estimate for solutions of Riccati equations, with which we show that the sequence of construoted solutions has a Limit which is a solution to the original Riccati equation.