In this paper we consider MPC for a class of constrained discrete-time Markovian switching systems consisting of a family of nonlinear stochastic subsystems whose nonlinear stochastic term for a particular mode is described by its statistical properties. The additive nonlinearity of the subsystems is allowed to contain state, input, and independent noise vectors. It is allowed so that hard constraints are imposed on the input manipulated variables. The results obtained are applied to the dynamic investment portfolio selection problem for a financial market with switching modes subject to hard constraints on trading amounts taking into account the presence of market frictions, Our approach is tested on a set of real data from the Russian Stock Exchange MICEX. (C) 2017 Elsevier Ltd. All rights reserved.