Karim El  Moutaouakil, Kaoutar  Senhaji, Mohamed  Ettaouil, 
    A Robust Neural Network Approach for the Portfolio Selection Problem
Basing on New Rational Models,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 3,
    2019,
    Pages 675-683,
    ISSN 1816-949x,
    jeasci.2019.675.683,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.675.683)
    Abstract: The portfolio management is a very important problem in the econometric field. In this research, we
propose a new model by adding a new constraint to the Markowitz’s Models to avoid the investigation into
the assets of a negative return. Because of its effectiveness, continuous hopfield network is used to solve the
proposed models. In this regard, we construct an original energy function that makes a compromise between
the risk, profit and cardinality constraints. To ensure the equilibrium point feasibility, the parameters of the
energy function are chosen based on a consistence mathematical results; In addition, the slop of the activation
functions is chosen such that the behavior of each neuron is almost leaner. We compare our method to several
other ones, basing on real financial data. The proposed method produces the best solutions.
    Keywords: Portfolio problem;mean-variance;semi-variance;efficient frontier;hopfield neural networks;energy
function;Genetic algorithm