  This paper is concerned with a stochastic linear-quadratic (LQ) optimal
control problem on infinite time horizon, with regime switching, random
coefficients, and cone control constraint. To tackle the problem, two new
extended stochastic Riccati equations (ESREs) on infinite time horizon are
introduced. The existence of the nonnegative solutions, in both standard and
singular cases, is proved through a sequence of ESREs on finite time horizon.
Based on this result and some approximation techniques, we obtain the optimal
state feedback control and optimal value for the stochastic LQ problem
explicitly. Finally, we apply these results to solve a lifetime portfolio
selection problem of tracking a given wealth level with regime switching and
portfolio constraint.
