Fractal Theory and Its Financial Applications for Improving the Quality of Professional Training at The Higher School of Economics

The article presents the didactic potential of modern fractal theory and its financial applications related to modeling and forecasting of financial performance. The purpose of the study is to identify the main content and methodological features of the disclosure of fractal theory and its financial applications in the practice of professional training of students of economic universities. The results of the analysis of popular science and scientific literature on fractal theory and its applications allowed us to clarify its didactic potential in the system of higher economic education. The use of elements of the technological approach at the Higher School of Economics made it possible to construct the educational process on fractal theory and its financial applications in the form of a system of micro-goals of the basic level, which serves as a guideline for organizing and planning the results of educational and cognitive activity of students of the Bachelor of Economics. Involvement of various techniques and methods of the theory of pedagogical technologies based on the establishment and study of the laws of the educational process as the results of scientific knowledge of the process of human education, as well as financial faculties of the Plekhanov Russian University of Economics and the Financial University under the Government of the Russian Federation as the basis of experimental work allowed to identify the attitude of students to fractal theory and its applications, to conduct primary testing of fractal theory as a new element of the content of mathematical training, as well as directions for improving the educational process in applied mathematical disciplines. Special attention is paid to the mechanisms of development of students’ competencies in the field of decision-making in conditions of risk and uncertainty, a meaningful choice of methods for studying financial situations that require optimal decisions. A system of micro-goals of the basic level is presented, consisting of thirteen micro-goals and allowing a teacher of mathematical disciplines to design invariant content in the field of fractal theory and its applications for higher economic school. Attention is also focused on the need to update the methodological work of teachers of mathematical disciplines on the design and construction of the educational process. Including the base level set by the system of micro-goals presented in this article, which regulates the educational process in the language of educational and cognitive activity of a student of an economic bachelor’s degree. It is noted that the complex transformations taking place in modern society affect various aspects of social, financial and economic relations, increase the requirements for the methodological, design and technological culture of a teacher of mathematical disciplines. The prospects of the study include the development of criteria for the selection of digital tools to support fractal theory and its financial applications as an element of the content of professional training, as well as the development and subsequent implementation of a program of additional professional education on alternative approaches to decision-making in the financial sector. The content of the article can be useful for the implementation of applied, professional strengthening of the teaching of compulsory mathematical disciplines for students studying in the direction of “Economics” of various directions (Mathematical methods in economics, World Economy, Finance and Credit, etc.), and for the formulation of new academic disciplines of students’ choice, as well as improving the content of programs of additional professional education related to the quantitative justification of decisions.