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Mathematics
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Mathematical Methods and Statistics for Economics, Actuarial Science and Finance
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Mathematical Methods and Statistics for Economics, Actuarial Science and Finance

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

Deadline for manuscript submissions: 10 July 2026 | Viewed by 2884

Special Issue Editor

Dr. Min Shu

E-Mail Website
Guest Editor
Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA
Interests: applied statistics; quantitative finance; time series analysis; machine learning; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We will be publishing a Special Issue on the “Mathematical Methods and Statistics for Economics, Actuarial Science and Finance”. Through this Issue, we aim to attract papers covering the myriad facets of the analysis and modeling of economics, actuarial science, and finance. The rapid advances in these fields, combined with the increasing complexity of financial markets and economic systems, necessitate the development and application of sophisticated analytical tools. This Special Issue will provide a platform for researchers and practitioners to share their insights and contribute to the advancement of these crucial areas.

This Special Issue welcomes high-quality, original research papers on a wide range of topics, including (but not limited to) the following:

  • Econometrics;
  • Financial Mathematics;
  • Actuarial Modeling;
  • Mathematical Economics;
  • Quantitative Finance;
  • Statistical Analysis and Modeling;
  • Time Series Analysis;
  • Optimization Techniques;
  • Machine Learning in Finance;
  • Big Data Analytics for Economic and Financial Applications.

This Special Issue encourages the submission of various types of papers, including theoretical papers that introduce novel mathematical or statistical frameworks, empirical studies that apply advanced analytical techniques to real-world economic, actuarial, or financial problems, as well as methodological papers that propose new algorithms or computational methods.

Dr. Min Shu
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

  • econometrics
  • financial mathematics
  • actuarial modeling
  • mathematical economics
  • quantitative finance
  • statistical analysis and modeling
  • time series analysis
  • optimization techniques
  • machine learning in finance
  • big data analytics for economic and financial applications

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

17 pages, 6312 KB  
Article
Black–Litterman Portfolio Optimization with Dynamic CAPM via ABC-MCMC
by Sebastián Flández, Rolando Rubilar-Torrealba, Karime Chahuán-Jiménez, Hanns de la Fuente-Mella and Claudio Elórtegui-Gómez
Mathematics 2025, 13(20), 3265; https://doi.org/10.3390/math13203265 - 12 Oct 2025
Viewed by 1523
Abstract
The present research proposes a methodology for portfolio construction that integrates the Black–Litterman model with expected returns generated through simulations under dynamic Capital Asset Pricing Model (CAPM) with conditional betas, estimated via Approximate Bayesian Computation Markov Chain Monte Carlo (ABC-MCMC). Bayesian estimation enables [...] Read more.
The present research proposes a methodology for portfolio construction that integrates the Black–Litterman model with expected returns generated through simulations under dynamic Capital Asset Pricing Model (CAPM) with conditional betas, estimated via Approximate Bayesian Computation Markov Chain Monte Carlo (ABC-MCMC). Bayesian estimation enables the incorporation of volatility regimes and the adjustment of each asset’s sensitivity to the market, thereby delivering expected returns that more accurately reflect the structural state of the assets compared to historical methods. This strategy is applied to the United States stock market, and the results suggest that the Black–Litterman portfolio performs competitively against portfolios optimised using the classic Markowitz model, even maintaining the same fixed weights throughout the month. Specifically, it has been demonstrated to outperform the minimum variance portfolio with regard to cumulative return and attains a Sharpe ratio that approaches the Markowitz maximum Sharpe portfolio, although it does so with a distinct and more concentrated asset allocation. It has been observed that, while the maximum return portfolio attains the highest absolute profit, it does so at the expense of significantly higher volatility. Full article
(This article belongs to the Special Issue Mathematical Methods and Statistics for Economics, Actuarial Science and Finance)
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16 pages, 1021 KB  
Article
Stochastic SO(2) Lie Group Method for Approximating Correlation Matrices
by Melike Bildirici, Yasemen Ucan and Ramazan Tekercioglu
Mathematics 2025, 13(9), 1496; https://doi.org/10.3390/math13091496 - 30 Apr 2025
Cited by 3 | Viewed by 725
Abstract
Standard correlation analysis is one of the frequently used methods in financial markets. However, this matrix can give erroneous results in the conditions of chaos, fractional systems, entropy, and complexity for the variables. In this study, we employed the time-dependent correlation matrix based [...] Read more.
Standard correlation analysis is one of the frequently used methods in financial markets. However, this matrix can give erroneous results in the conditions of chaos, fractional systems, entropy, and complexity for the variables. In this study, we employed the time-dependent correlation matrix based on isospectral flow using the Lie group method to assess the price of Bitcoin and gold from 19 July 2010 to 31 December 2024. Firstly, we showed that the variables have a chaotic and fractional structure. Lo’s rescaled range (R/S) and the Mandelbrot–Wallis method were used to determine fractionality and long-term dependence. We estimated and tested the d parameter using GPH and Phillips’ estimators. Renyi, Shannon, Tsallis, and HCT tests determined entropy. The KSC determined the evidence of the complexity of the variables. Hurst exponents determined mean reversion, chaos, and Brownian motion. Largest Lyapunov and Hurst exponents and entropy methods and KSC found evidence of chaos, mean reversion, Brownian motion, entropy, and complexity. The BDS test determined nonlinearity, and later, the time-dependent correlation matrix was obtained by using the stochastic SO(2) Lie group. Finally, we obtained robustness check results. Our results showed that the time-dependent correlation matrix obtained by using the stochastic SO(2) Lie group method yielded more successful results than the ordinary correlation and covariance matrix and the Spearman correlation and covariance matrix. If policymakers, financial managers, risk managers, etc., use the standard correlation method for economy or financial policies, risk management, and financial decisions, the effects of nonlinearity, fractionality, entropy, and chaotic structures may not be fully evaluated or measured. In such cases, this can lead to erroneous investment decisions, bad portfolio decisions, and wrong policy recommendations. Full article
(This article belongs to the Special Issue Mathematical Methods and Statistics for Economics, Actuarial Science and Finance)
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