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The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use…

Portfolio Management · Quantitative Finance 2020-04-20 Jinwoo Park

When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the…

Machine Learning · Computer Science 2025-10-28 Jayanta Mandi , Marianne Defresne , Senne Berden , Tias Guns

Portfolio optimization involves determining the optimal allocation of portfolio assets in order to maximize a given investment objective. Traditionally, some form of mean-variance optimization is used with the aim of maximizing returns…

Artificial Intelligence · Computer Science 2024-03-26 Fernando Acero , Parisa Zehtabi , Nicolas Marchesotti , Michael Cashmore , Daniele Magazzeni , Manuela Veloso

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

Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks. Instead of merely optimizing for predictive accuracy, DFL trains models to directly minimize…

Machine Learning · Computer Science 2026-03-10 Aymeric Capitaine , Maxime Haddouche , Eric Moulines , Michael I. Jordan , Etienne Boursier , Alain Durmus

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…

Statistical Finance · Quantitative Finance 2023-04-19 Taras Bodnar , Nestor Parolya , Wolfgang Schmid

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…

Applications · Statistics 2018-04-03 Emmanuelle Jay , Eugénie Terreaux , Jean-Philippe Ovarlez , Frédéric Pascal

This study presents the Adaptive Minimum-Variance Portfolio (AMVP) framework and the Adaptive Minimum-Risk Rate (AMRR) metric, innovative tools designed to optimize portfolios dynamically in volatile and nonstationary financial markets.…

Econometrics · Economics 2025-01-28 Ayush Jha , Abootaleb Shirvani , Ali Jaffri , Svetlozar T. Rachev , Frank J. Fabozzi

In many automated planning applications, action costs can be hard to specify. An example is the time needed to travel through a certain road segment, which depends on many factors, such as the current weather conditions. A natural way to…

Artificial Intelligence · Computer Science 2024-08-27 Jayanta Mandi , Marco Foschini , Daniel Holler , Sylvie Thiebaux , Jorg Hoffmann , Tias Guns

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor's risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning…

Portfolio Management · Quantitative Finance 2020-07-21 Yusuke Uchiyama , Kei Nakagawa

Stock portfolio optimization is the process of constant re-distribution of money to a pool of various stocks. In this paper, we will formulate the problem such that we can apply Reinforcement Learning for the task properly. To maintain a…

Machine Learning · Computer Science 2020-12-14 Le Trung Hieu

Financial markets are inherently non-stationary, with shifting volatility regimes that alter asset co-movements and return distributions. Standard portfolio optimization methods, typically built on stationarity or regime-agnostic…

Portfolio Management · Quantitative Finance 2025-10-20 Yiyao Zhang , Diksha Goel , Hussain Ahmad , Claudia Szabo

This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms,…

Portfolio Management · Quantitative Finance 2025-11-17 Emmanuel Lwele , Sabuni Emmanuel , Sitali Gabriel Sitali

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio…

Portfolio Management · Quantitative Finance 2025-08-22 Maciej Wysocki , Paweł Sakowski

This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. Specifically, we impose an autoregressive dynamic structure on MVP processes, which…

Methodology · Statistics 2023-10-23 Donggyu Kim , Minseog Oh

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…

Portfolio Management · Quantitative Finance 2016-01-20 Liusha Yang , Romain Couillet , Matthew R. McKay

When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a…

Machine Learning · Computer Science 2026-01-29 Noah Schutte , Grigorii Veviurko , Krzysztof Postek , Neil Yorke-Smith

The majority of standard approaches to financial portfolio optimization (PO) are based on the mean-variance (MV) framework. Given a risk aversion coefficient, the MV procedure yields a single portfolio that represents the optimal trade-off…

Portfolio Management · Quantitative Finance 2024-02-27 Bruno Gašperov , Marko Đurasević , Domagoj Jakobovic

Propose a deep learning driven multi factor investment model optimization method for risk control. By constructing a deep learning model based on Long Short Term Memory (LSTM) and combining it with a multi factor investment model, we…

Computational Finance · Quantitative Finance 2025-07-02 Ruisi Li , Xinhui Gu

Decision-focused learning (DFL) trains a machine learning (ML) model to predict parameters of an optimization problem, to directly minimize decision regret, i.e., maximize decision quality. Gradient-based DFL requires computing the…

Machine Learning · Computer Science 2025-08-26 Jayanta Mandi , Ali İrfan Mahmutoğulları , Senne Berden , Tias Guns