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This paper is concerned with a stochastic linear-quadratic (LQ) optimalcontrol problem on infinite time horizon, with regime switching, randomcoefficients, and cone control constraint. To tackle the problem, two newextended stochastic Riccati equations (ESREs) on infinite time horizon areintroduced. The existence of the nonnegative solutions, in both standard andsingular cases, is proved through a sequence of ESREs on finite time horizon.Based on this result and some approximation techniques, we obtain the optimalstate feedback control and optimal value for the stochastic LQ problemexplicitly. Finally, we apply these results to solve a lifetime portfolioselection problem of tracking a given wealth level with regime switching andportfolio constraint.

Constrained stochastic LQ control on infinite time horizon with regime switching