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Entropy, Artificial Intelligence and the Financial Markets

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 15 June 2026 | Viewed by 29522

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Prof. Dr. Gil Cohen

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Department of Management, Western Galilee Academic College, P.O. Box 2125, Acre 2412101, Israel
Interests: investment; financial markets; corporate finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Financial markets are evolving rapidly, reshaping global investment opportunities. AI is revolutionizing finance by enhancing decision-making, improving predictive accuracy, and optimizing risk management. This transformation fosters efficiency, transparency, and accessibility across markets.

One key contribution of AI is its ability to enrich the investment process with valuable information. Traditional models struggle with processing vast, unstructured data, but AI extracts insights from alternative sources such as news sentiment, social media, and economic indicators, improving market predictions and asset valuations. By reducing noise and identifying hidden patterns, AI enhances informational efficiency, enabling more informed investment decisions.

AI also plays a crucial role in managing entropy in financial systems. Entropy representing uncertainty and randomness in markets can lead to inefficiencies and volatility. AI-driven models help to quantify and mitigate entropy by detecting trends, forecasting risks, and refining asset pricing. This allows investors to navigate uncertainty more effectively and optimize capital allocation.

We request research papers exploring AI’s impact on financial forecasting, risk analysis, and decision-making. Studies on AI’s role in asset pricing, anomaly detection, and algorithmic trading across various financial instruments are highly encouraged. Both theoretical and empirical contributions that offer fresh insights into AI and finance are welcome.

Prof. Dr. Gil Cohen
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

AI and financial innovations
AI and business information
AI and trading
AI and market forecasts
AI and risk analysis
AI and fintech
AI real estate information and pricing
AI and technical analysis

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Published Papers (10 papers)

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Research

27 pages, 13300 KB

Open AccessArticle

Information-Entropic Deep Learning with Gaussian Process Regularisation for Uncertainty-Aware Quantitative Trading

by Feng Lin and Huaping Sun

Entropy 2026, 28(5), 485; https://doi.org/10.3390/e28050485 - 23 Apr 2026

Viewed by 107

Abstract

Quantitative trading systems require predictive models that simultaneously deliver accurate forecasts, calibrated uncertainty quantification, and actionable risk measures. This paper proposes an information-theoretic semiparametric regression framework combining a convolutional neural network–Transformer (CNN–Transformer) network for nonlinear temporal dependencies with a Gaussian process (GP) prior for residual autocorrelation and calibrated predictive distributions. Three theoretical results are established: an identifiability theorem guarantees joint recoverability of the nonparametric and GP components; a consistency theorem showing that the penalised maximum likelihood estimator converges at a rate

n^{- 1 / (2 + d_{eff})}

; and a coverage theorem proving asymptotic nominal coverage of the GP’s credible intervals. The framework enables an entropy-regulated trading module where predictive differential entropy informs position sizing via an uncertainty-penalised Kelly criterion, Kullback–Leibler divergence quantifies model uncertainty, and CVaR-constrained optimisation controls the tail risk. Simulations show the method outperforms the CNN, long short-term memory (LSTM), Transformer, XGBoost, random forest, least absolute shrinkage and selection operator (LASSO), and standard GP regression approaches. Backtesting on four Chinese A-share stocks yielded annualised returns of 15.9–22.4% with Sharpe ratios of 0.49–0.62, maximum drawdowns below 15%, and daily 95% CVaR reductions of 28–31% relative to a full-Kelly baseline, confirming both predictive accuracy and risk management effectiveness. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

26 pages, 27074 KB

Open AccessArticle

Entropy-Driven Adaptive Decomposition and Linear-Complexity Score Attention: An AI-Powered Framework for Crude Oil Financial Market Forecasting

by Jiale He, Chuanming Ma, Shouyi Wang, Yifan Zhai and Qi Tang

Entropy 2026, 28(4), 392; https://doi.org/10.3390/e28040392 - 1 Apr 2026

Viewed by 455

Abstract

The crude oil market has obvious financial entropy, and there are characteristics such as continuous uncertainty, multi-scale fluctuations and nonlinear state transitions. These characteristics bring challenges to the traditional prediction method. In this context, in order to improve the accuracy of energy financial market prediction, this study proposes an artificial intelligence-driven hybrid prediction framework, ALA-VMD-CASA. This framework is divided into three stages. First, with the goal of minimizing envelope entropy, ALA is introduced to adaptively optimize the hyperparameters of VMD, so as to generate informative sub-modes with reduced entropy. Next, the parallel prediction of each sub-mode is carried out by using the score attention mechanism based on the CNN autoencoder, and its linear time complexity can capture volatility clustering and sudden price fluctuations. Finally, the final price prediction is generated through the aggregation component. The empirical experiment of Brent crude oil spot prices from 2010 to 2025 shows that the ALA-VMD-CASA framework is superior to benchmark models such as ARIMA, RW, RWWD, LSTM, GRU, Transformer and Informer. Compared with the best standalone model, the proposed framework reduces the mean square error by more than 63% and obtains a perfect win rate in expanding-window evaluations. These results prove that the proposed framework is effective and robust for modeling financial entropy and improving energy price forecasting. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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32 pages, 5770 KB

Open AccessArticle

Digital Leadership, Information Entropy, and Stock Price Volatility: Evidence from CEO Social Media Behavior

by Yutong Zou, Jingqian Tian, Yunfan Zhang, Guangping Shi and Xiao Cai

Entropy 2026, 28(2), 200; https://doi.org/10.3390/e28020200 - 10 Feb 2026

Viewed by 803

Abstract

In the digital economy, social media has become a critical channel through which corporate executives communicate with investors, thereby influencing market expectations and price dynamics. This study examines how CEO social media behavior affects stock price volatility from an information-theoretic perspective combined with deep learning methods. Using Lei Jun (Xiaomi) and Elon Musk (Tesla) as contrasting cases, we analyze executive communication under transactional and transformational leadership styles. Emotional tone, thematic alignment, and diffusion intensity are extracted using BERT and LDA, and incorporated into a Long Short-Term Memory (LSTM) model to forecast short-term stock price movements. To interpret the mechanism behind the predictive results, we introduce a novel metric: Semantic Resonance Dissipation Entropy (SRE). Derived from Kullback–Leibler divergence, this indicator measures the informational friction between executive semantic output and market attention. The empirical analysis shows that incorporating these high-dimensional semantic features significantly improves volatility prediction. Moreover, leadership style is closely associated with distinct entropic regimes: Transactional leadership corresponds to relatively stable semantic patterns and low entropy, whereas transformational leadership is associated with higher entropy and greater semantic dispersion. Following Musk’s acquisition of Twitter, the previously unstable information environment evolved into a persistent structural factor priced by the market. These findings suggest that the economic impact of digital leadership depends on limiting information dissipation to ensure signal clarity in financial markets. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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25 pages, 1436 KB

Open AccessArticle

Entropy-Augmented Forecasting and Portfolio Construction at the Industry-Group Level: A Causal Machine-Learning Approach Using Gradient-Boosted Decision Trees

by Gil Cohen, Avishay Aiche and Ron Eichel

Entropy 2026, 28(1), 108; https://doi.org/10.3390/e28010108 - 16 Jan 2026

Viewed by 713

Abstract

This paper examines whether information-theoretic complexity measures enhance industry-group return forecasting and portfolio construction within a machine-learning framework. Using daily data for 25 U.S. GICS industry groups spanning more than three decades, we augment gradient-boosted decision tree models with Shannon entropy and fuzzy entropy computed from recent return dynamics. Models are estimated at weekly, monthly, and quarterly horizons using a strictly causal rolling-window design and translated into two economically interpretable allocation rules, a maximum-profit strategy and a minimum-risk strategy. Results show that the top performing strategy, the weekly maximum-profit model augmented with Shannon entropy, achieves an accumulated return exceeding 30,000%, substantially outperforming both the baseline model and the fuzzy-entropy variant. On monthly and quarterly horizons, entropy and fuzzy entropy generate smaller but robust improvements by maintaining lower volatility and better downside protection. Industry allocations display stable and economically interpretable patterns, profit-oriented strategies concentrate primarily in cyclical and growth-sensitive industries such as semiconductors, automobiles, technology hardware, banks, and energy, while minimum-risk strategies consistently favor defensive industries including utilities, food, beverage and tobacco, real estate, and consumer staples. Overall, the results demonstrate that entropy-based complexity measures improve both economic performance and interpretability, yielding industry-rotation strategies that are simultaneously more profitable, more stable, and more transparent. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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21 pages, 503 KB

Open AccessArticle

Flexible Target Prediction for Quantitative Trading in the American Stock Market: A Hybrid Framework Integrating Ensemble Models, Fusion Models and Transfer Learning

by Keyue Yan, Zihuan Yue, Chi Chong Wu, Qiqiao He, Jiaming Zhou, Zhihao Hao and Ying Li

Entropy 2026, 28(1), 84; https://doi.org/10.3390/e28010084 - 11 Jan 2026

Cited by 3 | Viewed by 2164

Abstract

Stock price prediction is a core challenge in quantitative finance. While machine learning has advanced the modeling of complex financial time series, existing methods often rely on single-target predictions, underutilize multidimensional market information, and are disconnected from practical trading systems. To address these gaps, this research develops a hybrid machine learning framework for flexible target forecasting and systematic trading of major American technology stocks. The framework integrates Ensemble Models (AdaBoost, Decision Tree, LightGBM, Random Forest, XGBoost) with Fusion Models (Voting, Stacking, Blending) and introduces a Transfer Learning method enhanced by Dynamic Time Warping to facilitate knowledge sharing across assets, improving robustness. Focusing on ten key stocks, we forecast three distinct momentum indicators: next-day Closing Price Difference, Moving Average Difference, and Exponential Moving Average Difference. Empirical results demonstrate that the proposed Transfer Learning approach achieves superior predictive performance and trading simulations confirm that strategies based on these predicted momentum signals generate substantial returns. This research demonstrates that the proposed hybrid machine learning framework can mitigate the high information entropy inherent in financial markets, offering a systematic and practical method for integrating machine learning with quantitative trading. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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27 pages, 500 KB

Open AccessArticle

TARFA: A Novel Approach to Targeted Accounting Range Factor Analysis for Asset Allocation

by Jose Juan de Leon and Francesca Medda

Entropy 2026, 28(1), 52; https://doi.org/10.3390/e28010052 - 31 Dec 2025

Viewed by 766

Abstract

The valuation of companies has long been a cornerstone of financial analysis and investment decision-making, offering critical frameworks for investors to gauge a firm’s worth and evaluate the relative value of future income streams within a specific industry or sector. In this work we propose a new valuation framework by integrating traditional and modern valuation approaches, providing actionable insights for investors and analysts seeking to optimize asset allocation and portfolio performance. We introduce a novel framework (TARFA) to comparable company valuation by identifying investor-preferred return-driving points for accounting-based factors. Through an analysis of 68 commonly used accounting measures, the study identifies three key factors that drive superior returns. The results of the TARFA framework demonstrate that both general and sector-specific models consistently outperformed population returns, with the general model showing superior performance in broader market contexts. The study also highlights the stability of key financial ratios over time and introduces the Relative Equity Score, further enhancing the model’s ability to identify undervalued equities. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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26 pages, 4789 KB

Open AccessArticle

EMAT: Enhanced Multi-Aspect Attention Transformer for Financial Time Series Forecasting

by Yingjun Chen, Wenfeng Shen, Han Liu and Xiaolin Cao

Entropy 2025, 27(10), 1029; https://doi.org/10.3390/e27101029 - 1 Oct 2025

Cited by 4 | Viewed by 2211

Abstract

Financial time series prediction remains a challenging task due to the inherent non-stationarity, noise, and complex temporal dependencies present in market data. Traditional forecasting methods often fail to capture the multifaceted nature of financial markets, where temporal proximity, trend dynamics, and volatility patterns simultaneously influence price movements. To address these limitations, this paper proposes the Enhanced Multi-Aspect Transformer (EMAT), a novel deep learning architecture specifically designed for stock market prediction. EMAT incorporates a Multi-Aspect Attention Mechanism that simultaneously captures temporal decay patterns, trend dynamics, and volatility regimes through specialized attention components. The model employs an encoder–decoder architecture with enhanced feed-forward networks utilizing SwiGLU activation, enabling superior modeling of complex non-linear relationships. Furthermore, we introduce a comprehensive multi-objective loss function that balances point-wise prediction accuracy with volatility consistency. Extensive experiments on multiple stock market datasets demonstrate that EMAT consistently outperforms a wide range of state-of-the-art baseline models, including various recurrent, hybrid, and Transformer architectures. Our ablation studies further validate the design, confirming that each component of the Multi-Aspect Attention Mechanism makes a critical and quantifiable contribution to the model’s predictive power. The proposed architecture’s ability to simultaneously model these distinct financial characteristics makes it a particularly effective and robust tool for financial forecasting, offering significant improvements in accuracy compared to existing approaches. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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17 pages, 3264 KB

Open AccessArticle

Hybrid CNN-LSTM-GNN Neural Network for A-Share Stock Prediction

by Junhao Dong and Shi Liang

Entropy 2025, 27(8), 881; https://doi.org/10.3390/e27080881 - 20 Aug 2025

Cited by 4 | Viewed by 7035

Abstract

Optimization of stock selection strategies has been a topic of interest in finance. Although deep learning models have demonstrated superior performance over traditional methods, there are still shortcomings. For example, previous studies do not provide enough explanation for feature selection and usually use features such as closing price directly to make predictions; for example, most studies predict the trend of multiple stock indices or only individual stocks, which is difficult to be directly applied to actual stock selection. In this paper, a multivariate hybrid neural network model CNN-LSTM-GNN (CLGNN) for stock prediction is proposed, in which the CNN and the LSTM modules analyze the local and the whole, respectively, while the multivariate time series GNN module is added to explore the potential relationships between the data through the graph learning, graph convolutional, and temporal convolutional layers. CLGNN analyzes the potential relationships between the data based on the returns to classify stocks, and then develops a stock selection strategy, and directly outputs the returns and stock codes. In this paper, a hybrid filter approach based on entropy and Pearson correlation is proposed for feature selection, and experiments are conducted on all stocks in the CSI All Share Index (CSI); the results show that among multiple models, the returns obtained when the features of daily return, turnover rate, relative strength index, volume, and forward adjusted closing price are used as inputs are all the highest, and the return obtained by CLGNN is even higher than that of the other models (e.g., TCN, Transformer, etc.). Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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37 pages, 12521 KB

Open AccessArticle

Modeling Stylized Facts in FX Markets with FINGAN-BiLSTM: A Deep Learning Approach to Financial Time Series

by Dong-Jun Kim, Do-Hyeon Kim and Sun-Yong Choi

Entropy 2025, 27(6), 635; https://doi.org/10.3390/e27060635 - 14 Jun 2025

Cited by 4 | Viewed by 2596

Abstract

We propose the financial generative adversarial network–bidirectional long short-term memory (FINGAN-BiLSTM) model to accurately reproduce the complex statistical properties and stylized facts, namely, heavy-tailed behavior, volatility clustering, and leverage effects observed in the log returns of the foreign exchange (FX) market. The proposed model integrates a bidirectional LSTM (BiLSTM) into the conventional FINGAN framework so that the generator, discriminator, and predictor networks simultaneously incorporate both past and future information, thereby overcoming the information loss inherent in unidirectional LSTM architectures. Experimental results, assessed using metrics such as the Kolmogorov–Smirnov statistic, demonstrate that FINGAN-BiLSTM effectively mimics the distributional and dynamic patterns of actual FX data. In particular, the model significantly reduces the maximum cumulative distribution discrepancy in assets with high standard deviations and extreme values, such as the Canadian dollar (CAD) and the Mexican Peso (MXN), while precisely replicating dynamic features like volatility clustering and leverage effects, thereby outperforming conventional models. The findings suggest that the proposed deep learning–based forecasting model holds significant promise for practical applications in financial risk assessment, derivative pricing, and portfolio optimization, and they highlight the need for further research to enhance its generalization capabilities through the integration of exogenous economic variables. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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17 pages, 917 KB

Open AccessArticle

Artificial Intelligence Models for Predicting Stock Returns Using Fundamental, Technical, and Entropy-Based Strategies: A Semantic-Augmented Hybrid Approach

by Gil Cohen, Avishay Aiche and Ron Eichel

Entropy 2025, 27(6), 550; https://doi.org/10.3390/e27060550 - 23 May 2025

Cited by 5 | Viewed by 11205

Abstract

This study examines the effectiveness of combining semantic intelligence drawn from large language models (LLMs) such as ChatGPT-4o with traditional machine-learning (ML) algorithms to develop predictive portfolio strategies for NASDAQ-100 stocks over the 2020–2025 period. Three different predictive frameworks––fundamental, technical, and entropy-based––are tested through examination of novel combinations of ML- and LLM-derived semantic metrics. The empirical results reveal a considerable divergence in optimal blending methods across the methodologies; namely, the technical methodology exhibits the best performance when using only ML predictions, with around 1978% cumulative returns with monthly rebalancing. In contrast, the fundamental methodology achieves its full potential when it is based primarily on LLM-derived semantic insights. The Entropy methodology is improved by a balanced combination of both semantic and ML signals, thus highlighting the potential of LLMs to improve predictive power by offering interpretative context for complex market interactions. These findings highlight the strategic importance of tailoring the semantic–algorithmic fusion to suit the nature of the predictive data and the investment horizon, with significant implications for portfolio management and future research in financial modeling. Full article

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)

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