The asset allocation decision is often considered as a trade-off between maximizing the expected return of a portfolio and minimizing the portfolio risk. The riskiness is evaluated in terms of variance of the portfolio return, so that it is fundamental to consider correctly the variance of its components and their correlations. The evidence of the heteroskedastic behavior of the returns and the time-varying relationships among the portfolio components have recently shifted attention to the multivariate GARCH models with time varying correlation. In this work we insert a particular Markov Switching dynamics in some Dynamic Correlation models to consider the abrupt changes in correlations affecting the assets in different ways. This class of models is very general and provides several specifications, constraining some coefficients. The models are applied to solve a sectorial asset allocation problem and are compared with alternative models.