A Comprehensive Review of Financial Fraud Anomaly Detection Using Mathematical and Computational Methods

Amit Patel

Authors

Amit Patel Author

Keywords:

Financial Fraud Detection, Anomaly Detection, Machine Learning, Mathematical Modeling, Artificial Intelligence, Computational Methods, Financial Analytics.

Abstract

The rapid growth of digital banking and online financial transactions has increased the risk of financial fraud, including credit card fraud, identity theft, and money laundering. Traditional fraud detection methods often face challenges in identifying complex and evolving fraudulent activities. Anomaly detection has emerged as an effective approach for recognizing unusual transaction patterns and preventing financial losses. Mathematical methods such as statistical analysis, probability theory, and optimization techniques, along with computational approaches including machine learning, deep learning, and artificial intelligence, play a vital role in modern fraud detection systems.

This review examines the major mathematical and computational methods used for financial fraud anomaly detection. It analyzes traditional statistical techniques, machine learning algorithms, deep learning models, and hybrid approaches, highlighting their applications, advantages, and limitations. The review finds that AI-driven and hybrid models generally provide higher detection accuracy and better adaptability to emerging fraud patterns. Future research directions include explainable AI, federated learning, blockchain integration, and real-time fraud detection systems.

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