2025 1(48) 26

Mathematical Modeling of Financial Violation Detection in the Economic Forensics System to Ensure Enterprise Security in the Digital Economy

Samira Tymofiivna Piletska
Dr. of Economics, Prof.
ORCID https://orcid.org/0000-0002-3638-3002
e-mail: 0508486185@ukr.net,
State University “Kyiv Aviation Institute”,
Sergii Oleksiiovych Kolesnikov
Candidate of Physics and Mathematics, Assoc. Prof.,
ORCID https://orcid.org/0000-0002-9538-8858,
LLC “Technical University “Metinvest Polytechnic”, Zaporizhzhia

Citation Format
Piletska, S. Т., Kolesnikov, S. О. (2025). Mathematical Modeling of Financial Violation Detection in the Economic Forensics System to Ensure Enterprise Security in the Digital Economy. Vіsnyk ekonomіchnoі nauky Ukraіny, 1 (48), рр. 165-169. https://doi.org/10.37405/1729-7206.2025.1(48).165-169

Language
 Ukrainian

Resume
In today’s dynamic economic environment, characterized by rapid digitization of the financial sector and exponential growth in transaction data volumes, traditional methods of detecting financial crimes (fraud, accounting manipulation, money laundering) are becoming increasingly ineffective. Classic approaches to economic forensics, focused primarily on retrospective analysis of primary documentation and ratio analysis, are unable to provide timely and reliable identification of complex, hidden abuse schemes in real time. The purpose of this article is to develop and test a mathematical model for detecting violations in enterprise financial data as an element of a modern economic forensics system in the context of digitalization.
A conceptual approach is proposed that positions economic forensics as an independent field of knowledge aimed at ensuring the legal legitimacy of financial analysis and strengthening the cyber financial security of an enterprise. Particular attention is paid to the development of a mathematical model for the automated detection of financial violations. The model is based on the principles of unsupervised learning and semi-supervised learning. A key element is the use of Mahalanobis distance for each transaction, which allows calculating the degree of deviation of a particular transaction from the “normal” distribution, taking into account the correlations between numerous financial indicators and their dispersion. The formalized approach involves constructing a metric space of transactions, determining the center of gravity of normal behavior and the covariance matrix, and setting a threshold value for identifying anomalies. Thanks to dynamic updating of estimates, the model is able to detect statistical outliers and structural changes in behavioral patterns.
In addition to Mahalanobis distance, the study considers the application of other machine learning methods (clustering – k-means, DBSCAN; anomaly detection – Z-score, Isolation Forest, autoencoders), as well as natural language processing (NLP) for analyzing unstructured data (contracts, correspondence), which allows detecting suspicious wording and changes in communication.
The study also focuses on the challenges of implementing such models, in particular the problems of interpreting results (false positives), limited transparency of “black box” algorithms, as well as the need to comply with regulatory and ethical aspects (data protection, GDPR) and significant investments in technological infrastructure and qualified human resources.
Conclusions. The study confirms that mathematical modeling and digital tools are a key area of development for economic forensics, providing businesses with effective mechanisms for strengthening financial security and ensuring sustainable development in a dynamic digital economy.

Keywords
forensics, economic forensics, economic security, digital economy, innovation, enterprise, risk, model, mathematical modeling.

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Full Text (.pdf)

Received: 22.04.2025
Accepted: 16.05.2025
Published: 19.06.2025