In modern world, the digitalisation of financial relations, the development of innovative technologies, and the emergence and use of cryptocurrencies for payments lead to an increase in the number of cyber frauds in the financial sector and their intellectualisation, increasing the illegal outflow of funds abroad. Ineffective decisions and inaction in counteracting these threats lead to large-scale negative consequences of both financial and social nature. The purpose of this study is to implement economic and mathematical modelling of the effectiveness of the national system for combatting cyber fraud and legalisation of criminal proceeds, which is based on the use of survival analysis methods. The study provides a bibliometric analysis of publications on the effectiveness of cyber fraud and combatting the legalisation of illegal funds, by building a bibliometric map of keywords, using VOSviewer software. This allowed identifying 7 clusters of basic categories of cyber fraud analysis, and changes in the vectors of research scientists showed a visual map of the contextual-temporal measurement of research into the effectiveness of cyber fraud in the publications of the Scopus database. The paper examines the effectiveness of the national system for combatting cyber fraud and money laundering based on survival tables. As a result of the study, the effectiveness of the national system for combatting cyber fraud and money laundering was analysed based on the Kaplan-Meier method. The study identified the dependences of the effectiveness of the national system for combatting cyber fraud and legalisation of criminal proceeds on the time interval after the discovery of violations. The practical value of applying the developed model is to form an analytical basis for further management decisions by the National Bank of Ukraine, the State Financial Monitoring Service, and the Security Service of Ukraine in terms of the effectiveness of the national system to combat cyber fraud and legalisation of criminal proceeds and the need to adjust it

The article is devoted to the current topic of analysis of mathematical models for countering cyber fraud in banks. This problem is due to the security risks growth in the banking system, which are formed by fraudsters' cyberattacks and cybercrimes implementation. Therefore, the priority task for cyberbanking security is the application of modern mathematical methods to analyse the sources of cyber attacks, identify threats and losses in the banking services market, identify cyber-attacks and assess the scenario of potential cyber risk, etc. The article analyses the most widespread types of cyber fraud: social engineering, phishing, stalking, farming, DoS attacks, online fraud, potentially unwanted programs, etc. The study also considered a model of cognitive computing and detection of suspicious transactions in banking cyber-physical systems based on quantum computing in BCPS for the post-quantum era. The advantages, disadvantages and results of the model are defined. Predictive modelling is proposed to detect fraud in real-time by analysing incoming bank transactions with payment cards. Within the framework of this method, such models are used for the classification of fraud detection as logistic regression, a decision tree, and a narrower technique - a random forest decision tree. The study also considered using the harmonic search algorithm in neural networks to improve fraud detection in the banking system. It is found that although this model has the advantage of learning ability based on past behaviour, there are difficulties in the long-term processing of many neural networks. The stages of model implementation are also given. In addition, the modelling of credit card fraud detection is based on using two types of models: supervised and unsupervised. Supervised models include logistic regression, K-nearest neighbours, and extreme gradient boosting. The one-class support vector model, restricted Boltzmann model, and generative-competitive network are considered among uncontrolled generative models.

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