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Mathematical and Computational Methods in Financial and Risk Forecasting
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Mathematical and Computational Methods in Financial and Risk Forecasting

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

Deadline for manuscript submissions: closed (31 January 2026) | Viewed by 8280

Special Issue Editors

Prof. Dr. Kuang-Hsun Shih

E-Mail Website
Guest Editor
Doctorate Program in Intelligent Banking and Finance, CTBC Business School, Tainan 709, Taiwan
Interests: intelligent finance; banking operation and management; risk analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shu-Ping Lin

E-Mail Website
Guest Editor
Department of Banking and Finance, CTBC Business School, Tainan 709, Taiwan
Interests: research methods; data science and AI; service market and management; FINTECH; performance evaluation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yi-Hsien Wang

E-Mail Website
Guest Editor
Doctorate Program in Intelligent Banking and Finance, CTBC Business School, Tainan 709, Taiwan
Interests: financial econometrics; investment management; decision science; risk analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to this Special Issue, which focuses on the integration of advanced mathematical and computational techniques in financial innovation and risk management. The rapid evolution of blockchain technology and the cryptocurrency market has transformed financial asset management, introducing new complexities and challenges. Understanding the risk characteristics and opportunities arising from the convergence of traditional and digital finance is an essential area of academic and practical inquiries. This Special Issue addresses these developments and their implications for portfolio management, risk assessment, and regulatory compliance.

Moreover, it aims to advance our knowledge in applying mathematical and computational methods to financial and risk management challenges. It aligns with the journal’s focus on combining theoretical and practical insights to solve real-world problems. Topics of interest include innovative models and algorithms for portfolio optimization, derivative pricing, and financial econometrics. Contributions emphasizing interdisciplinary approaches that integrate finance, mathematics, computer science, and data analytics are particularly encouraged.

In this Special Issue, we welcome original research articles and reviews that explore, but are not limited to, the following themes:

  • Derivative pricing and trading strategies;
  • Portfolio optimization and ETF analysis;
  • Risk analytics and forecasting in finance;
  • Artificial intelligence and machine learning applications;
  • Computational methods in financial innovation;
  • Digital asset management.

We look forward to receiving your contributions.

Prof. Dr. Kuang-Hsun Shih
Prof. Dr. Shu-Ping Lin
Prof. Dr. Yi-Hsien Wang
Guest Editors

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
  • cryptocurrency
  • financial risk forecasting
  • derivative pricing
  • portfolio optimization
  • computational finance
  • artificial intelligence
  • intelligent banking and finance
  • digital asset management

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

21 pages, 1214 KB  
Article
Bayesian vs. Evolutionary Optimization for Cryptocurrency Perpetual Trading: The Role of Parameter Space Topology
by Petar Zhivkov and Juri Kandilarov
Mathematics 2026, 14(5), 761; https://doi.org/10.3390/math14050761 - 25 Feb 2026
Viewed by 736
Abstract
Hyperparameter optimization for cryptocurrency trading strategies encounters distinct challenges owing to continuous operation, volatility rates 3–4 times higher than equity indices, and price dynamics influenced by market sentiment. Bayesian optimization (Tree-Structured Parzen Estimator, TPE) and evolutionary algorithms (Differential Evolution, DE) are great for [...] Read more.
Hyperparameter optimization for cryptocurrency trading strategies encounters distinct challenges owing to continuous operation, volatility rates 3–4 times higher than equity indices, and price dynamics influenced by market sentiment. Bayesian optimization (Tree-Structured Parzen Estimator, TPE) and evolutionary algorithms (Differential Evolution, DE) are great for machine learning, but there are not many systematic comparisons for trading cryptocurrencies. This research evaluates Random Sampling, TPE, and DE through 36 factorial experiments, comprising 3 trading strategies (3, 4, and 5 hyperparameters) × 3 optimizers × 4 cryptocurrency pairs (BTC/USDT, ETH/USDT, INJ/USDT, SOL/USDT), resulting in 14,400 backtesting trials with walk-forward validation. TPE won 75% of strategy–asset pairs (9 of 12), reaching 90% of optimal performance within 13–17% of trial budgets. We find strategy-specific optimizer compatibility: mean-reversion strategies show DE underperformance independent of topology (−1% to −8%), whereas trend-following strategies show consistent DE competitiveness across assets (+13% to +37%). Most notably, for the same strategy, parameter space topology differs significantly between assets (trend following: 4.6% viable on BTC to 82% on ETH = 17.8×; mean reversion: 10.8% on ETH to 92% on SOL = 8.5×), indicating that topology results from strategy–asset interaction rather than intrinsic properties. Complete testing failures and widespread severe overfitting point to regime non-stationarity as a fundamental problem. Among the contributions are: (1) evidence shows that topological effects are dominated by optimizer–strategy compatibility (DE fails on mean-reversion strategies even in 92% viable spaces, but succeeds on trend-following strategies regardless of topology, spanning 13.6–82% viable spaces); (2) this is the first systematic Bayesian versus evolutionary comparison across 4 cryptocurrency assets; (3) parameter space topology emerges from strategy–asset interaction, varying up to 17.8-fold; and (4) single-period backtests inadequately identify parameter instability. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Financial and Risk Forecasting)
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35 pages, 5655 KB  
Article
Information Transmission Across Markets: Tail Risk Spillovers and Cross-Market Volatility Forecasting
by Shaocong Peng and Yun Shi
Mathematics 2026, 14(4), 686; https://doi.org/10.3390/math14040686 - 15 Feb 2026
Viewed by 419
Abstract
This paper examines tail risk spillovers and cross-market volatility forecasting between the U.S. equity market and the crude oil market. Using realized and implied volatility within a heterogeneous autoregressive (HAR) framework, we document asymmetric and time-varying tail risk transmission across the two markets. [...] Read more.
This paper examines tail risk spillovers and cross-market volatility forecasting between the U.S. equity market and the crude oil market. Using realized and implied volatility within a heterogeneous autoregressive (HAR) framework, we document asymmetric and time-varying tail risk transmission across the two markets. Motivated by these findings, we propose several cross-market volatility forecasting strategies, including direct information augmentation, threshold-based designs, forecast averaging, and transfer learning. The results show that incorporating cross-market information improves volatility forecasts primarily at medium and longer horizons, consistent with the forward-looking nature of implied volatility. Moreover, the relative effectiveness of different transmission mechanisms varies across markets, with transfer learning performing particularly well in the crude oil market. Overall, the findings highlight the importance of linking tail risk spillovers to volatility forecasting and demonstrate that flexible cross-market information transmission can enhance predictive performance across markets and horizons. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Financial and Risk Forecasting)
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29 pages, 3320 KB  
Article
Risk-Aware Crypto Price Prediction Using DQN with Volatility-Adjusted Rewards Across Multi-Period State Representations
by Otabek Sattarov and Fazliddin Makhmudov
Mathematics 2025, 13(18), 3012; https://doi.org/10.3390/math13183012 - 18 Sep 2025
Cited by 1 | Viewed by 4079
Abstract
Forecasting Bitcoin prices remains a complex task due to the asset’s inherent and significant volatility. Traditional reinforcement learning (RL) models often rely on a single observation from the time series, potentially missing out on short-term patterns that could enhance prediction performance. This study [...] Read more.
Forecasting Bitcoin prices remains a complex task due to the asset’s inherent and significant volatility. Traditional reinforcement learning (RL) models often rely on a single observation from the time series, potentially missing out on short-term patterns that could enhance prediction performance. This study presents a Deep Q-Network (DQN) model that utilizes a multi-step state representation, incorporating consecutive historical timesteps to reflect recent market behavior more accurately. By doing so, the model can more effectively identify short-term trends under volatile conditions. Additionally, we propose a novel reward mechanism that adjusts for volatility by penalizing large prediction errors more heavily during periods of high market volatility, thereby encouraging more risk-aware forecasting behavior. We validate the effectiveness of our approach through extensive experiments on Bitcoin data across minutely, hourly, and daily timeframes. The proposed model achieves notable results, including a Mean Absolute Percentage Error (MAPE) of 10.12%, Root Mean Squared Error (RMSE) of 815.33, and Value-at-Risk (VaR) of 0.04. These outcomes demonstrate the advantages of integrating short-term temporal features and volatility sensitivity into RL frameworks for more reliable cryptocurrency price prediction. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Financial and Risk Forecasting)
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28 pages, 5343 KB  
Article
Transformer-Based Downside Risk Forecasting: A Data-Driven Approach with Realized Downward Semi-Variance
by Yuping Song, Yuetong Zhang, Po Ning, Jiayi Peng, Chunyu Kao and Liang Hao
Mathematics 2025, 13(8), 1260; https://doi.org/10.3390/math13081260 - 11 Apr 2025
Cited by 1 | Viewed by 1960
Abstract
Realized downward semi-variance (RDS) has been realized as a key indicator to measure the downside risk of asset prices, and the accurate prediction of RDS can effectively guide traders’ investment behavior and avoid the impact of market fluctuations caused by price declines. In [...] Read more.
Realized downward semi-variance (RDS) has been realized as a key indicator to measure the downside risk of asset prices, and the accurate prediction of RDS can effectively guide traders’ investment behavior and avoid the impact of market fluctuations caused by price declines. In this paper, the RDS rolling prediction performance of the traditional econometric model, machine learning model, and deep learning model is discussed in combination with various relevant influencing factors, and the sensitivity analysis is further carried out with the rolling window length, prediction length, and a variety of evaluation methods. In addition, due to the characteristics of RDS, such as aggregation and jumping, this paper further discusses the robustness of the model under the impact of external events, the influence of emotional factors on the prediction accuracy of the model, and the results and analysis of the hybrid model. The empirical results show that (1) when the rolling window is set to 20, the overall prediction effect of the model in this paper is the best. Taking the Transformer model under SSE as an example, compared with the prediction results under the rolling window length of 5, 10, and 30, the RMSE improvement ratio reaches 24.69%, 15.90%, and 43.60%, respectively. (2) The multivariable Transformer model shows a better forecasting effect. Compared with traditional econometric, machine learning, and deep learning models, the average increase percentage of RMSE, MAE, MAPE, SMAPE, MBE, and SD indicators is 52.23%, 20.03%, 62.33%, 60.33%, 37.57%, and 18.70%, respectively. (3) In multi-step prediction scenarios, the DM test statistic of the Transformer model is significantly positive, and the prediction accuracy of the Transformer model remains stable as the number of prediction steps increases. (4) Under the impact of external events of COVID-19, the Transformer model has stability, and the addition of emotional factors can effectively improve the prediction accuracy. In addition, the model’s prediction performance and generalization ability can be further improved by stacked prediction models. An in-depth study of RDS forecasting is of great value to capture the characteristics of downside risks, enrich the financial risk measurement system, and better evaluate potential losses. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Financial and Risk Forecasting)
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