The powerful scientific and educational school "Modeling and Riskology in Economics" is recognized in Ukraine and abroad. The prerequisite for its creation was the works of the outstanding mathematician-economist Yevhen Slutsky, who taught at the Kyiv Commercial Institute (now Kyiv National Economic University named after Vadym Hetman) in 1913–1926.

The formation of the scientific school began in the 90s of the last century with the study of problems of analysis and assessment of risk in entrepreneurship. At its origins were such professors of KNEU as Terekhov, L., Nakonechnyi, S., Suslov, O., Sharapov, O., Vitlinskyi, V.. In different years, they headed the department, which is now called Mathematical Modeling and Statistics (MMS). In 1968, the textbook Terekhov, L. "Economic and Mathematical Methods" was published -, one of the first textbooks in the former USSR on economic and mathematical methods and models. A number of monographs, textbooks and teaching aids, in particular: "Economic Risk and Methods of its Measurement" by Vitlinskyi, V., Nakonechnyi, S., Sharapov, O. (1996); "Modeling of the Economy" by Vitlinskyi, V. (2003); "Riskology in Economics and Entrepreneurship " by Vitlinskyi, V., Velykoivanenko, H. (2004) found wide resonance in Ukraine and abroad.

Valdemar Vitlinskyi formulated the name of the scientific and educational school "Modeling and Riskology in Economics" and became its founder .

The following main scientific results ofVitlinskyi can be noted:

• the theoretical and methodological foundations of riskology (risk management) and the concept of its structuring as a systemically coordinated complex of mechanisms and economic and mathematical models have been significantly developed;
• it is substantiated that the quantitative measure of risk should take into account its dialectical objective-subjective structure, and a number of new indicators of quantitative risk assessment are proposed;
• a fuzzy method with AHP has been developed, as well as a game-based fuzzy method;
• the need to take into account asymmetry and kurtosis for assessing financial risks, tools for quantitative assessment of conditional "capital at risk" and possible extreme losses are substantiated;
• several new utility functions were constructed and substantiated;
• the conceptual provisions and tools for modeling economic objects, processes, and phenomena are summarized based on the application of systemic and synergistic approaches, the apparatus of nonlinear dynamics, and taking into account system characteristics;
• The need for generalization of methodological provisions is substantiated and a toolkit for complex pre-forecast analysis of time series is developed.

Valdemar Vitlinskyi made a significant contribution to the development of the scientific school and economic science in general.

D.Sc. in Economics, Prof. AndriyMatviychuk: developed a concept for building economic and mathematical models for identifying financial time dependencies and forecasting financial indicators taking into account the regularities of the development of economic systems; formed and substantiated a methodological approach to conducting a comprehensive analysis of the financial condition of enterprises (institutions) using the fuzzy logic apparatus; developed a conceptual approach to assessing the risk of tax evasion, distributing taxpayers by categories of attention and a methodology for forming a tax audit schedule; formulated methodological provisions for building a multi-level hierarchical system for quantitatively assessing the competitiveness of an enterprise based on the synthesis of fuzzy logic methods and neural networks.

D.Sc. in Economics, Prof. Olena Piskunova developed the concept of compositional uncertainty, which makes it possible to study the functioning of a small enterprise in conditions of uncertainty of a complex structure and build appropriate mathematical models. She proposed to distinguish between the systemic characteristics of the entrepreneur's decisions and the functioning of the enterprise.

D.Sc. in Economics Yurii Kolyada substantiated the concept of end-to-end adaptive modeling of the dynamics of a nonlinear economic system, which helps to achieve a more complete understanding of the adaptability of the economic mechanism in the conditions of a heterarchically changing topology of its structure, a combination of feedback loops of polar signs, goals and evaluation criteria.

Iryna Lukianenko made a significant contribution to the development of econometric modeling and its application to the analysis of modern problems of the Ukrainian economy. Andrii Kaminskyi developed theoretical and methodological provisions for mathematical modeling of financial risks, tools for their analysis and measurement. Petro Hrytsiuk made a theoretical generalization and proposed a new solution to the problem of forecasting indicators of the grain production system in Ukraine based on reversible cyclical dynamics. Andriy Skrypnyk contributed to the development of forecasting macroeconomic indicators. Eugene Afanasiev developed theoretical principles, methodologies and models for assessing and substantiating the development strategy of mining enterprises taking into account risk. A significant contribution to the development of the theory of stochastic processes and their application to solving practical economic problems was made by Candidate of Technical Sciences, Associate Professor Volodymyr Zhluktenko. The achievements of Candidate of Physical and Mathematical Sciences , Associate Professor Petro Verchenko , who worked on the problems of modeling and analysis of economic risk. Active work on modeling and optimization of economic processes in the agro-industrial complex taking into account risk was led by Candidate of Economic Sciences, Professor Stepan Nakonechnyi, under whose leadership 24 candidate theses were defended.

Today, the main areas of activity of the scientific school are:

• fundamental and applied research on mathematical modeling of economic processes and systems based on artificial intelligence, machine learning, and big data technologies ( big data ), knowledge mining ( data mining , data knowledge ) and classical statistical methods;
• modeling of economic sectors, living standards and social protection of the population, economic competitiveness, economic security, and foreign economic relations;
• development of mathematical models and expert systems for analysis and forecasting of commodity, financial, foreign exchange markets, and the monetary industry at the local and global levels.