  In finance industry portfolio construction deals with how to divide the
investors' wealth across an asset-classes' menu in order to maximize the
investors' gain. Main approaches in use at the present are based on variations
of the classical Markowitz model. However, recent evolutions of the world
market showed limitations of this method and motivated many researchers and
practitioners to study alternative methodologies to portfolio construction. In
this paper we propose one approach to optimal portfolio construction based on
recent results on stochastic reachability, which overcome some of the limits of
current approaches. Given a sequence of target sets that the investors would
like their portfolio to stay within, the optimal portfolio allocation is
synthesized in order to maximize the joint probability for the portfolio value
to fulfill the target sets requirements. A case study in the US market is given
which shows benefits from the proposed methodology in portfolio construction. A
comparison with traditional approaches is included.
