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Advances in Machine Learning Applied to Financial Economics

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A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: closed (31 July 2026) | Viewed by 18812

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Prof. Dr. Saejoon Kim

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Departments of Computer Science and Engineering, and Artificial Intelligence, Sogang University, Seoul 04107, Republic of Korea
Interests: machine learning; financial economics; asset pricing; factor models

Special Issue Information

Dear Colleagues,

Machine learning is ubiquitous in today’s society from web searches, object identification and text/speech translation to more sophisticated applications using generative artificial intelligence such as ChatGTP. Its far-reaching effect has influenced how financial mathematicians and economists conduct research complementing classical statistical approaches to the analysis of cross section and time series of returns. Machine learning applied to financial economics has become a hot topic in both academia and asset management industry reflected by the surge in the number of research articles on this topic, ranging from identification of patterns in returns and volatility to learning the efficient frontier, being published by both groups of participants. Recently, it has allowed for the establishment of improved asset pricing models, portfolio optimization and risk management techniques.

In light of recent attention to this topic, in this Special Issue, we seek advancements of machine learning techniques applied to the field of financial economics. Contributions to the areas of, but not limited to, estimation of asset pricing models, financial decision making under uncertainty with economic and financial models, identification of latent factors, portfolio optimization and risk management, statistical methods for financial market data, and time series prediction all employing various forms of machine learning are solicited. We pay particular interest to how machine learning techniques are incorporated to serve as new methods to solve problems in finance.

Prof. Dr. Saejoon Kim
Guest Editor

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Keywords

machine learning
deep learning
generative artificial intelligence
representation learning
asset pricing models and asset price dynamics
arbitrage pricing
option pricing
equilibrium-based pricing
high-frequency trading
optimal asset allocation and portfolios
factor models
latent factors
time series prediction
risk management
value at risk
volatility estimation
cross section of returns

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Published Papers (6 papers)

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Research

32 pages, 4720 KB

Open AccessArticle

Explainability-Guided Transformer Models for Hourly Cryptocurrency Forecasting: A Comparative Study with SHAP-Based Feature Refinement

by Zeynep Hilal Kilimci and Erçin Dinçer

Mathematics 2026, 14(18), 3402; https://doi.org/10.3390/math14183402 (registering DOI) - 19 Sep 2026

Abstract

Accurate cryptocurrency price forecasting represents an important yet challenging problem in financial time-series analysis due to the highly volatile, nonlinear, and noise-sensitive nature of digital asset markets. Although transformer-based architectures have recently demonstrated strong capabilities in temporal sequence modeling, their behavior under high-frequency cryptocurrency dynamics and the role of explainability-guided feature refinement remain insufficiently explored. To address this gap, this study presents a comprehensive transformer-based forecasting framework for hourly cryptocurrency price prediction and investigates the impact of explainability-guided feature optimization on forecasting performance, robustness, and interpretability. Five transformer architectures—Vanilla Transformer, Informer, Autoformer, Reformer, and Temporal Fusion Transformer (TFT)—are systematically evaluated across five major cryptocurrency assets: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Dogecoin (DOGE), and Ripple (XRP). The experimental framework employs Open, High, Low, Close, and Volume (OHLCV) data together with a broad set of engineered technical indicators and evaluates model performance using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R²). To improve interpretability and reduce feature redundancy, SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) are integrated directly into the forecasting pipeline. Based on the resulting explanations, asset-specific feature subsets are constructed, and all models are subsequently retrained using the refined feature representations. The results show that explainability-guided feature refinement provides compact, model-aware, and interpretable feature subsets with competitive forecasting performance; however, its effect on prediction accuracy is dependent on the cryptocurrency asset, transformer architecture, retained feature subset size, and market conditions. Additional robustness, sensitivity, alternative feature-selection, and statistical significance analyses indicate that the SHAP–LIME Top-15 subset should be interpreted as a conservative dimensionality-reduction strategy rather than a universally optimal feature-selection rule. The findings further reveal that transformer architectures incorporating sparse attention, decomposition mechanisms, or gating structures generally provide stronger performance than the Vanilla Transformer under highly volatile hourly market conditions. Overall, the proposed framework demonstrates that combining transformer-based forecasting with explainability-guided feature refinement can support interpretable and parsimonious high-frequency financial time-series modeling, while highlighting the importance of evaluating robustness, feature-selection sensitivity, and statistical variability alongside average forecasting errors. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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38 pages, 10353 KB

Open AccessArticle

Nonlinear Effects of Machine Learning-Assisted Investment Decisions on Investor Behavior and Asset Pricing Efficiency

by Ziheng Xu and Wan Liu

Mathematics 2026, 14(15), 2683; https://doi.org/10.3390/math14152683 - 24 Jul 2026

Viewed by 515

Abstract

Machine learning technologies are increasingly embedded in financial decision-making processes, yet their influence on investor behavior and market efficiency remains insufficiently understood. This study investigates how machine learning-assisted investment decisions affect investor behavioral biases and asset pricing efficiency and whether these effects exhibit nonlinear characteristics. Using investor-level trading records, survey data, and market data from the Chinese A-share market (N = 12,846 investors; 3876 questionnaires; 3 million+ transactions), we construct measures of machine learning adoption intensity, investor behavioral biases, and asset pricing efficiency. Employing fixed-effects models, instrumental-variable estimation (2SLS), and mediation analysis, we examine the behavioral and market consequences of machine learning adoption. The results reveal a significant U-shaped relationship between machine learning adoption intensity and investor behavioral biases (inflection point: AIDI* = 0.731), and an inverted U-shaped relationship between AI market penetration and asset pricing efficiency (threshold: AIPM* = 0.733). Investor behavioral bias mediates 26.34% of the total effect of AI adoption on pricing efficiency. Moderate adoption reduces behavioral biases by improving information processing and decision quality, whereas excessive reliance on algorithmic recommendations generates automation bias and weakens investors’ independent judgment. At the market level, machine learning adoption exhibits an inverted U-shaped relationship with asset pricing efficiency. While moderate adoption enhances information incorporation into prices and reduces pricing deviations, excessive market penetration may induce algorithmic homogeneity and diminish efficiency gains. Furthermore, investor behavioral bias serves as an important transmission mechanism linking machine learning adoption to asset pricing outcomes. Heterogeneity analyses indicate that institutional investors benefit more from machine learning tools than individual investors, and the effects are stronger during periods of high market uncertainty. These findings provide new evidence on the optimal adoption of machine learning in financial markets and offer practical implications for intelligent investment platforms, investor education, and financial regulation. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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25 pages, 3558 KB

Open AccessArticle

AGNAE: An Augmented-Driven Graph Network with Adaptive Exploration for Real-Time Fraud Detection in Dynamic Financial Networks

by Limu Qiu

Mathematics 2026, 14(10), 1626; https://doi.org/10.3390/math14101626 - 11 May 2026

Viewed by 668

Abstract

Real-time fraud detection has become a critical component in ensuring the security and stability of the digital financial ecosystem. However, existing methods struggle to adapt to the highly dynamic and adversarial nature of modern financial fraud, where malicious actors constantly evolve their strategies to evade detection. To address the dual challenges of complex topological relationships and severe concept drift, we propose the Augmented-Driven Graph Network with Adaptive Exploration (AGNAE). First, this paper introduces an augmented graph neural network tailored for financial transaction graphs, which dynamically models the heterogeneous interactions between transacting entities to capture complex, hidden fraud rings. Second, rather than relying on static classifiers, we rigorously formulate the real-time detection process as a sequential decision-making problem. This paper introduces a deep reinforcement learning agent equipped with an adaptive exploration mechanism to continuously update detection strategies, striking an optimal balance between exploiting known fraud patterns and exploring emerging mutations. Furthermore, a novel joint loss function is designed to synergize topological representation learning with the agent’s long-term financial reward optimization. Extensive experiments on the real-world for IEEE-CIS and FDAD-20 datasets demonstrate that AGNAE significantly outperforms state-of-the-art baselines. Crucially, despite its sophisticated architecture, AGNAE maintains an inference latency of 1.12 ms per transaction, fully satisfying the stringent computational requirements of real-world financial infrastructures. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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35 pages, 2479 KB

Open AccessFeature PaperArticle

Integrating Vision Transformer and Time–Frequency Analysis for Stock Volatility Prediction

by Myungjin Wooh and Poongjin Cho

Mathematics 2025, 13(23), 3787; https://doi.org/10.3390/math13233787 - 25 Nov 2025

Cited by 3 | Viewed by 5475

Abstract

Financial market volatility prediction remains challenging due to data nonlinearity and non-stationarity. Existing quantitative approaches struggle to capture multi-scale information embedded in time series, while convolutional neural network (CNN)-based image approaches primarily emphasize local feature extraction, whereas Vision Transformers (ViTs) more directly capture global dependencies through self-attention. To address these limitations, we propose TF-ViTNet, a dual-path hybrid model that integrates time–frequency scalogram generated via Continuous Wavelet Transform (CWT) with ViTs for volatility prediction. While time–frequency analysis has been widely adopted in prior studies, the application of ViTs to CWT-based scalograms within parallel architecture provides a new perspective for capturing global spatiotemporal structures in financial volatility. The model employs a parallel architecture where a Vision Transformer pathway learns global spatiotemporal patterns from scalograms while a Long Short-Term Memory (LSTM) pathway captures temporal characteristics from technical indicators, with both streams integrated at the final stage for volatility prediction. Empirical analysis using NASDAQ and S&P 500 index data from 2010 to 2024 demonstrates that TF-ViTNet consistently outperforms LSTM models using numerical data alone and existing benchmarks. In parallel architectures, Vision Transformers capture global patterns in scalograms more effectively than CNNs, achieving significant performance improvements, particularly for NASDAQ. The model maintains stable predictive power even during high volatility regimes, demonstrating strong potential as a risk management tool. Data augmentation improves performance for the stable S&P 500 market but degrades results for the volatile NASDAQ market, emphasizing the need for market-specific augmentation strategies tailored to underlying signal-to-noise characteristics. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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21 pages, 543 KB

Open AccessArticle

Estimating Asset Pricing Models in the Presence of Cross-Sectionally Correlated Pricing Errors

by Hyuksoo Kim and Saejoon Kim

Mathematics 2024, 12(21), 3442; https://doi.org/10.3390/math12213442 - 4 Nov 2024

Viewed by 2268

Abstract

In this study, we propose an adversarial learning approach to the asset pricing model estimation problem which aims to find estimates of factors and loadings that capture time-series covariations while minimizing the worst-case cross-sectional pricing errors. The proposed estimator is defined by a novel min-max optimization problem in which finding a solution is known to be difficult. This contrasts with other related estimators that admit a well-defined analytic solution but do not effectively account for correlations among the pricing errors. To this end, we propose an approximate algorithm based on the alternating optimization procedure and empirically demonstrate that our proposed adversarial estimation framework outperforms other existing factor models, especially when the explanatory power of the pricing model is limited. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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21 pages, 1997 KB

Open AccessArticle

Enhancing Portfolio Optimization: A Two-Stage Approach with Deep Learning and Portfolio Optimization

by Shiguo Huang, Linyu Cao, Ruili Sun, Tiefeng Ma and Shuangzhe Liu

Mathematics 2024, 12(21), 3376; https://doi.org/10.3390/math12213376 - 29 Oct 2024

Cited by 11 | Viewed by 8548

Abstract

The portfolio selection problem has been a central focus in financial research. A complete portfolio selection process includes two stages: stock pre-selection and portfolio optimization. However, most existing studies focus on portfolio optimization, often overlooking stock pre-selection. To address this problem, this paper presents a novel two-stage approach that integrates deep learning with portfolio optimization. In the first stage, we develop a stock trend prediction model for stock pre-selection called the AGC-CNN model, which leverages a convolutional neural network (CNN), self-attention mechanism, Graph Convolutional Network (GCN), and k-reciprocal nearest neighbors (k-reciprocal NN). Specifically, we utilize a CNN to capture individual stock information and a GCN to capture relationships among stocks. Moreover, we incorporate the self-attention mechanism into the GCN to extract deeper data features and employ k-reciprocal NN to enhance the accuracy and robustness of the graph structure in the GCN. In the second stage, we employ the Global Minimum Variance (GMV) model for portfolio optimization, culminating in the AGC-CNN+GMV two-stage approach. We empirically validate the proposed two-stage approach using real-world data through numerical studies, achieving a roughly 35% increase in Cumulative Returns compared to portfolio optimization models without stock pre-selection, demonstrating its robust performance in the Average Return, Sharp Ratio, Turnover-adjusted Sharp Ratio, and Sortino Ratio. Full article

(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)

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