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Mathematics
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Advances in Machine Learning Applied to Financial Economics
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Advances in Machine Learning Applied to Financial Economics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: 31 July 2026 | Viewed by 15998

Special Issue Editor

Prof. Dr. Saejoon Kim

E-Mail Website
Guest Editor
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

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. Mathematics is an international peer-reviewed open access semimonthly 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

  • 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 (4 papers)

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Research

25 pages, 3558 KB  
Article
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 265
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 [...] Read more.
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  
Article
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
Viewed by 4607
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 [...] Read more.
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  
Article
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 2070
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 [...] Read more.
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  
Article
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 9 | Viewed by 8021
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 [...] Read more.
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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