  This paper is concerned with a discrete-time mean-field stochastic
linear-quadratic optimal control problem arose from financial application.
Through matrix dynamical optimization method, a group of linear feedback
controls is investigated. The problem is then reformulated as an operator
stochastic linear-quadratic optimal control problem by a sequence of bounded
linear operators over Hilbert space, the optimal control with six algebraic
Riccati difference equations is obtained by backward induction. The two above
approaches are proved to be coincided by the classical method of completing the
square. Finally, after discussing the solution of the problem under
multidimensional noises, a financial application example is given.
