  In this work, we consider the optimal portfolio selection problem under hard
constraints on trading volume amounts when the dynamics of the risky asset
returns are governed by a discrete-time approximation of the Markov-modulated
geometric Brownian motion. The states of Markov chain are interpreted as the
states of an economy. The problem is stated as a dynamic tracking problem of a
reference portfolio with desired return. We propose to use the model predictive
control (MPC) methodology in order to obtain feedback trading strategies. Our
approach is tested on a set of a real data from the radically different
financial markets: the Russian Stock Exchange MICEX, the New York Stock
Exchange and the Foreign Exchange Market (FOREX).
