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Mathematics
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Probability Statistics and Quantitative Finance
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Probability Statistics and Quantitative Finance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 20 October 2025 | Viewed by 753

Special Issue Editor

Dr. Jieming Zhou

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Interests: financial engineering and risk management; stochastic control problems in financial insurance; financial statistics

Special Issue Information

Dear Colleagues,

This Special Issue explores the critical role of probability and statistics in advancing quantitative finance. As financial markets grow increasingly complex, the application of probabilistic models and statistical methods has become essential for understanding market dynamics, managing risks, and optimizing investment strategies. This Special Issue brings together cutting-edge research and practical insights on topics such as asset pricing, risk management, portfolio optimization, high-frequency trading, and market microstructure analysis. It also highlights the integration of machine learning and big data analytics in financial decision-making. By showcasing innovative approaches and real-world applications, this Special Issue aims to bridge the gap between theoretical advancements and practical challenges in quantitative finance. Researchers and practitioners are invited to submit their work, fostering a deeper understanding of how probability and statistics can drive more accurate predictions, efficient strategies, and robust financial systems. Submissions are encouraged to address both foundational theories and emerging trends, offering valuable perspectives for academics and industry professionals alike.

Dr. Jieming Zhou
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • asset pricing
  • risk management
  • portfolio optimization
  • high-frequency trading
  • market microstructure
  • machine learning in finance
  • option pricing
  • economics
  • finance
  • financial data analytics
  • stochastic models
  • derivatives pricing
  • behavioral finance
  • supply chain finance

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

Published Papers (3 papers)

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Research

9 pages, 359 KiB  
Article
On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process
by Rattiya Meesa, Ratinan Boonklurb and Phiraphat Sutthimat
Mathematics 2025, 13(12), 1948; https://doi.org/10.3390/math13121948 - 12 Jun 2025
Abstract
We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, [...] Read more.
We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally, we demonstrate that the same approach extends to a broad family of non-affine, time-varying diffusions, providing a general framework for obtaining transition PDFs and moments in advanced models. Full article
(This article belongs to the Special Issue Probability Statistics and Quantitative Finance)
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26 pages, 620 KiB  
Article
Optimal Investment Based on Performance Measure and Stochastic Benchmark Under PI and Position Constraints
by Chengzhe Wang, Congjin Zhou and Yinghui Dong
Mathematics 2025, 13(11), 1846; https://doi.org/10.3390/math13111846 - 2 Jun 2025
Viewed by 190
Abstract
We consider the portfolio selection problem faced by a manager under the performance ratio with position and portfolio insurance (PI) constraints. By making use of a dual control method in an incomplete market setting, we find the unique pricing kernel in the presence [...] Read more.
We consider the portfolio selection problem faced by a manager under the performance ratio with position and portfolio insurance (PI) constraints. By making use of a dual control method in an incomplete market setting, we find the unique pricing kernel in the presence of closed convex cone control constraints. Then, following the same arguments as in the complete market case, we derive the explicit form of the optimal investment strategy by combining the linearization method, the Lagrangian method, and the concavification technique. Full article
(This article belongs to the Special Issue Probability Statistics and Quantitative Finance)
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22 pages, 2700 KiB  
Article
A Novel Forecasting Framework for Carbon Emission Trading Price Based on Nonlinear Integration
by Rulin Gao and Jingyun Sun
Mathematics 2025, 13(10), 1624; https://doi.org/10.3390/math13101624 - 15 May 2025
Viewed by 260
Abstract
The complex features of carbon price, such as volatility and nonlinearity, pose a serious challenge to accurately predict it. To this end, this paper proposes a novel forecasting framework for carbon emission trading price based on nonlinear integration, including feature selection, deep learning [...] Read more.
The complex features of carbon price, such as volatility and nonlinearity, pose a serious challenge to accurately predict it. To this end, this paper proposes a novel forecasting framework for carbon emission trading price based on nonlinear integration, including feature selection, deep learning and model combination. Firstly, the historical carbon price series are collected and collated, and the factors affecting the carbon price are analyzed. Secondly, the data are downscaled and the input variables are screened using the max-relevance and min-redundancy. Then, the three integrated learning models are combined with the neural network model through nonlinear integration to construct a hybrid prediction model, and the best performing combined model is obtained. Finally, interval prediction is realized on the basis of point prediction. The experimental results show that the prediction model outperforms other comparative models in terms of prediction accuracy, stability and statistical hypothesis testing, and has good prediction performance. In summary, the hybrid prediction model proposed in this paper can not only provide high-precision carbon market price prediction for government and enterprise decision makers, but also help investors optimize their trading strategies and improve their returns. Full article
(This article belongs to the Special Issue Probability Statistics and Quantitative Finance)
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