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A continuous-time hidden Markov model for mean-variance portfolio optimization

We study a mean-variance portfolio selection problem under a hidden Markov regime-switching Black-Scholes-Merton economy with parameter uncertainty. By exploiting the separation principle, we solve the mean-variance portfolio selection problem and the filtering/estimation problem separately. An explicit solution to the mean-variance problem is derived using the stochastic maximum principle. Robust filters of the chain and robust-based EM algorithm for unknown model parameters are developed.