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A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client…

Optimization and Control · Mathematics 2018-10-26 Jize Zhang , Tim Leung , Aleksandr Aravkin

We investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and…

Other Condensed Matter · Physics 2008-12-02 Franco Busetti

In this paper, a heuristic method based on TabuSearch and TokenRing Search is being used in order to solve the Portfolio Optimization Problem. The seminal mean-variance model of Markowitz is being considered with the addition of cardinality…

Portfolio Management · Quantitative Finance 2022-12-01 Taylan Kabbani

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Andrea Schaerf

In this paper we apply a heuristic method based on artificial neural networks in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance…

Neural and Evolutionary Computing · Computer Science 2007-07-30 Alberto Fernandez , Sergio Gomez

This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf…

Econometrics · Economics 2026-03-18 Davit Gondauri

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number…

Computational Engineering, Finance, and Science · Computer Science 2023-07-11 Alexander Nikiporenko

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such…

Optimization and Control · Mathematics 2019-06-25 Lorenz M. Roebers , Aras Selvi , Juan C. Vera

In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The…

Computational Engineering, Finance, and Science · Computer Science 2014-04-15 Mahdi Moeini

This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by…

Optimization and Control · Mathematics 2022-12-22 Ken Kobayashi , Yuichi Takano , Kazuhide Nakata

This paper explores the practical approach to portfolio selection methods for investments. The study delves into portfolio theory, discussing concepts such as expected return, variance, asset correlation, and opportunity sets. It also…

Portfolio Management · Quantitative Finance 2024-10-16 Carlos Minutti-Martinez

Portfolio optimization is a critical area in finance, aiming to maximize returns while minimizing risk. Metaheuristic algorithms were shown to solve complex optimization problems efficiently, with Genetic Algorithms and Particle Swarm…

Portfolio Management · Quantitative Finance 2025-03-21 Hang Kin Poon

In this paper we propose and discuss different 0-1 linear models in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios to track indexes, together with other…

Portfolio Management · Quantitative Finance 2020-03-19 Juan Francisco Monge

As the number of credit card users has increased, detecting fraud in this domain has become a vital issue. Previous literature has applied various supervised and unsupervised machine learning methods to find an effective fraud detection…

Neural and Evolutionary Computing · Computer Science 2023-06-05 Anahita Farhang Ghahfarokhi , Taha Mansouri , Mohammad Reza Sadeghi Moghadam , Nila Bahrambeik , Ramin Yavari , Mohammadreza Fani Sani

Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean-Variance Optimization model unable to correctly…

Optimization and Control · Mathematics 2021-03-03 Justo Puerto , Federica Ricca , Moisés Rodríguez-Madrena , Andrea Scozzari

The portfolio optimization problem is a critical issue in asset management and has long been studied. Markowitz's mean-variance model has fundamental limitations, such as the assumption of a normal distribution for returns and sensitivity…

Statistical Mechanics · Physics 2025-10-28 Keita Takahashi , Tetsuro Abe , Yasuhito Nakamura , Ryo Hidaka , Shuta Kikuchi , Shu Tanaka

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean…

Portfolio Management · Quantitative Finance 2019-05-08 Francesco Cesarone , Andrea Scozzari , Fabio Tardella

A lot of problems, from fields like sparse signal processing, statistics, portfolio selection, and machine learning, can be formulated as a cardinality constraint optimization problem. The cardinality constraint gives the problem a discrete…

Optimization and Control · Mathematics 2025-04-08 Vikram Singh , Min Sun

The Markowitz mean-variance portfolio optimization model aims to balance expected return and risk when investing. However, there is a significant limitation when solving large portfolio optimization problems efficiently: the large and dense…

Portfolio Management · Quantitative Finance 2023-06-23 Cassidy K. Buhler , Hande Y. Benson

Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization…

Portfolio Management · Quantitative Finance 2023-08-23 Kapil Panda
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