N. Begashaw, Gurcan Comert, N. G. Medhin
Portfolio Selection Problem
Neural Parallel and Scientific Computations 33 (2025) 85-100

https://doi.org/10.46719/NPSC2025.33.05

ABSTRACT.
Given a set of securities or assets it is of interest to find an optimal way of investing in these
assets. What is optimal has to specified. The objective is to optimize the return consistent with the
specified objective. When there are several assets it is unlikely all the assets will increase if they are
correlated. It is necessary to diversify one’s assets for a secure return. To deal with the different
assets a combination of the assets should be considered with constraints as needed. One approach
is the Markowitz mean-variance model where the mean variance is minimized including constraints.
In this paper neural networks and machine learning are used to extend the ways of dealing with
portfolio asset allocation.

Portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is
imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search
and simulated annealing have been developed. The purpose of this paper is to consider a particular
neural network model, the Hopfield network, which has been used to solve some other optimisation
problems and apply it here to the portfolio selection problem, comparing the new results to those
obtained with previous heuristic algorithms. Although great success has been achieved for portfolio
analysis with the birth of Markowitz model, the demand for timely decision making has significantly
increased especially in recent years with the advancement of high frequency trading (HFT), which
combines powerful computing servers and the fastest Internet connection to trade at extremely high
speeds. This demand poses new challenges to portfolio solvers for real-time processing in the face of
time-varying parameters. Neural networks, as one of the most powerful machine learning tools has
seen great progress in recent years for financial data analysis and signal processing ([1], [14]). Using
computational methods, e.g., machine learning and data analytics, to empower conventional finance
is becoming a trend widely adopted in leading investment companies ([3]).

AMS (MOS) Subject Classification: 90C29, 90C30, 91A10, 65K05, 49N99, 49M37.

Keywords and phrases: Portfolio selection, Multiobjective problems, Neural networks.