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 September 2025 | Viewed by 181

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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
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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

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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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Published Papers (1 paper)

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Research

16 pages, 492 KiB  
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 (registering DOI) - 30 Apr 2025
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
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