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Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…

Machine Learning · Statistics 2025-05-16 Sarat Moka , Matias Quiroz , Vali Asimit , Samuel Muller

Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables…

Optimization and Control · Mathematics 2026-01-08 Pablo Thomassin , Guillaume Guerard , Sonia Djebali , Vincent Marc Lambert

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…

Physics and Society · Physics 2008-12-02 Stefano Ciliberti , Imre Kondor , Marc Mezard

In this paper, we document a novel machine learning based bottom-up approach for static and dynamic portfolio optimization on, potentially, a large number of assets. The methodology applies to general constrained optimization problems and…

Mathematical Finance · Quantitative Finance 2020-11-24 Qing Yang , Zhenning Hong , Ruyan Tian , Tingting Ye , Liangliang Zhang

The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…

Portfolio Management · Quantitative Finance 2012-06-04 Christoph Czichowsky , Martin Schweizer

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…

Portfolio Management · Quantitative Finance 2009-07-21 Giordano Pola , Gianni Pola

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

This work aims to deal with the optimal allocation instability problem of Markowitz's modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT)…

Statistical Finance · Quantitative Finance 2025-03-10 Andrés García-Medina , Benito Rodriguéz-Camejo

Since decades, the data science community tries to propose prediction models of financial time series. Yet, driven by the rapid development of information technology and machine intelligence, the velocity of today's information leads to…

Computational Finance · Quantitative Finance 2019-09-25 Giovanni Mariani , Yada Zhu , Jianbo Li , Florian Scheidegger , Roxana Istrate , Costas Bekas , A. Cristiano I. Malossi

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic…

Portfolio Management · Quantitative Finance 2013-05-13 Taras Bodnar , Nestor Parolya , Wolfgang Schmid

The main purpose of this study is the determination of the optimal length of the historical data for the estimation of statistical parameters in Markowitz Portfolio Optimization. We present a trading simulation using Markowitz method, for a…

Portfolio Management · Quantitative Finance 2012-10-23 Ertugrul Bayraktar , Ayse Humeyra Bilge

Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…

Computational Finance · Quantitative Finance 2024-08-16 Chung-Han Hsieh , Jie-Ling Lu

Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at…

Portfolio Management · Quantitative Finance 2024-11-22 Revant Nayar , Raphael Douady

Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…

Statistical Mechanics · Physics 2022-10-04 Álvaro Rubio-García , Juan José García-Ripoll , Diego Porras

In matter of Portfolio selection, we consider a generalization of the Markowitz Mean-Variance model which includes buy-in threshold constraints. These constraints limit the amount of capital to be invested in each asset and prevent very…

Computational Engineering, Finance, and Science · Computer Science 2016-11-18 Hoai An Le Thi , Mahdi Moeini

Online portfolio selection is an integral componentof wealth management. The fundamental undertaking is tomaximise returns while minimising risk given investor con-straints. We aim to examine and improve modern strategiesto generate higher…

Computational Engineering, Finance, and Science · Computer Science 2021-09-29 Matthew Kruger , Terence L. van Zyl , Andrew Paskaramoorthy

In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…

Optimization and Control · Mathematics 2025-09-23 Arturo Annunziata , Matteo Lapucci , Pieluigi Mansueto , Davide Pucci

This work discusses the benefits of constrained portfolio turnover strategies for small to medium-sized portfolios. We propose a dynamic multi-period model that aims to minimize transaction costs and maximize terminal wealth levels whilst…

Computational Finance · Quantitative Finance 2024-01-26 Nakul Upadhya , Alexandre Granzer-Guay

We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order…

Statistics Theory · Mathematics 2012-11-14 Noureddine El Karoui

Modeling and managing portfolio risk is perhaps the most important step to achieve growing and preserving investment performance. Within the modern portfolio construction framework that built on Markowitz's theory, the covariance matrix of…

Risk Management · Quantitative Finance 2021-10-28 Hengxu Lin , Dong Zhou , Weiqing Liu , Jiang Bian