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This paper is concerned with a stochastic linear-quadratic optimal controlproblem with regime switching, random coefficients, and cone controlconstraint. The randomness of the coefficients comes from two aspects: theBrownian motion and the Markov chain. Using It\^{o}'s lemma for Markov chain,we obtain the optimal state feedback control and optimal cost value explicitlyvia two new systems of extended stochastic Riccati equations (ESREs). We provethe existence and uniqueness of the two ESREs using tools includingmultidimensional comparison theorem, truncation function technique, logtransformation and the John-Nirenberg inequality. These results are thenapplied to study mean-variance portfolio selection problems with and withoutshort-selling prohibition with random parameters depending on both the Brownianmotion and the Markov chain. Finally, the efficient portfolios and efficientfrontiers are presented in closed forms.

Constrained stochastic LQ control with regime switching and application to portfolio selection