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In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian…

Computational Finance · Quantitative Finance 2023-05-22 Sumanjay Dutta , Shashi Jain

We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of…

Portfolio Management · Quantitative Finance 2026-04-07 Nolan Alexander , William Scherer

The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…

Mathematical Finance · Quantitative Finance 2021-10-15 Jean-Pierre Fouque , Ruimeng Hu , Ronnie Sircar

A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…

General Mathematics · Mathematics 2013-10-22 Cyrus Jahanchahi , Danilo P. Mandic

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

Methodology · Statistics 2017-04-25 Dimitris Bertsimas , Martin S. Copenhaver , Rahul Mazumder

The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable…

Portfolio Management · Quantitative Finance 2013-03-06 Xiangyu Cui , Xun Li , Duan Li

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the…

Statistics Theory · Mathematics 2025-07-11 Xuran Meng , Yuan Cao , Weichen Wang

For a covariance matrix coming from a factor model of returns, we investigate the relationship between the long-only global minimum variance portfolio and the asset exposures to the factors. In the case of a 1-factor model, we provide a…

Mathematical Finance · Quantitative Finance 2026-03-10 Nick L. Gunther , Alec N. Kercheval , Ololade Sowunmi

This paper introduces a hybrid framework for portfolio optimization that fuses Long Short-Term Memory (LSTM) forecasting with a Proximal Policy Optimization (PPO) reinforcement learning strategy. The proposed system leverages the predictive…

Machine Learning · Computer Science 2025-11-25 Jun Kevin , Pujianto Yugopuspito

We introduce a novel covariance estimator for portfolio selection that adapts to the non-stationary or persistent heteroskedastic environments of financial time series by employing exponentially weighted averages and nonlinearly shrinking…

Machine Learning · Statistics 2023-01-23 Vincent Tan , Stefan Zohren

Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study…

Quantum Physics · Physics 2023-05-03 Naman Jain , M Girish Chandra

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

Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the…

Statistical Mechanics · Physics 2015-06-25 Didier Sornette

Extant literature on fair pricing methods for actuarial contexts has primarily focused on the regression setting. While such approaches are well-suited to short-term products, it is unclear how they generalize to long-term products, whose…

Pricing of Securities · Quantitative Finance 2026-02-05 Hong Beng Lim , Mengyi Xu , Kenneth Q. Zhou

Sequential decision making, commonly formalized as optimization of a Markov Decision Process, is a key challenge in artificial intelligence. Two successful approaches to MDP optimization are reinforcement learning and planning, which both…

Machine Learning · Computer Science 2022-04-01 Thomas M. Moerland , Joost Broekens , Aske Plaat , Catholijn M. Jonker

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…

Mathematical Finance · Quantitative Finance 2022-11-29 Maxim Bichuch , Jean-Pierre Fouque

Solving portfolio management problems using deep reinforcement learning has been getting much attention in finance for a few years. We have proposed a new method using experts signals and historical price data to feed into our reinforcement…

Computational Finance · Quantitative Finance 2023-01-02 MohammadAmin Fazli , Mahdi Lashkari , Hamed Taherkhani , Jafar Habibi

In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance…

Portfolio Management · Quantitative Finance 2018-12-20 Mostafa Zandieh , Seyed Omid Mohaddesi

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…

Machine Learning · Statistics 2021-02-08 Zhu Li , Jean-Francois Ton , Dino Oglic , Dino Sejdinovic

We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component…

Machine Learning · Computer Science 2014-11-17 Mihalis A. Nicolaou , Stefanos Zafeiriou , Maja Pantic