Economic-mathematical Methods Research Articles

The modern mathematical models in economics and finance

With this article, we open a new section in this journal: the application of mathematical methods in economics and finance. A few topics we would like to discuss to get started are corporate finance, investments, business valuation, taxation, and ratings. We describe shortly mathematical models in these areas. In the field of corporate finance, we discuss the foundations of two main theories of capital structure, the Modigliani-Miller and the modern theory of Brusov-Filatova-Orekhova (BFO theory). We compare them and describe the differences between them and their results. In the field of investments, we describe two modern investment models: (1) with debt repayment at the end of the project and (2) with uniform debt repayment and discuss their properties and applications. In business valuation, we discuss the problems that exist in this area and ways to solve them. In rating methodology, a new approach is devoted to the rating of non–financial issuers, as well as to long–term and arbitrary duration project rating. The key factors of a new approach are the adequate use of discounting of financial flows virtually not used in existing rating methodologies, and the incorporation of rating parameters (financial "ratios") into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). This article is devoted to the analysis of the theoretical mathematical methods and models based on first principles. The novelty of this consideration is due to the fact that we are considering and discussing recently developed mathematical models in economics and finance.

FORECASTING INVESTMENT ACTIVITIES OF RAIL TRANSPORT ENTERPRISES USING TREND MODELS

The object of the study is the investment activity of railway transport enterprises. The purpose of the work is to forecast the investment activity of railway transport enterprises by using economic-mathematical methods and models, namely trend models. The information base of the study is the data of the State Statistics Service and the Ministry of Finance. It has been proven that the transport industry is one of the important branches of the national economy, which provides a logistic connection from the transportation of passengers to the transportation of goods. On the basis of economic-mathematical models (one-dimensional trend forecasting methods), a conceptual scheme for building forecast values of investment activities of railway transport enterprises has been suggested, with the help of which it is possible not only to forecast capital investments but also to propose measures for their increase. The results of investment forecasting by funding sources are given (at the expense of state budget funds, local budget funds, own funds of enterprises and organizations, bank loans and other loans, funds of foreign investors, funds of domestic investment companies, funds, etc., public funds for housing construction, other funding sources). Investments are distinguished by types of economic activity: "Transport, warehousing, postal and courier activities". The received forecast values of investment activity have been interpreted. Measures to increase the investment activity of railway transport enterprises are proposed. The results of the study can form the basis of the formation of the state strategy for the regional development of the country and, separately, in the development of plans and recommendations for the development of railway transport enterprises at different levels of management.

FORECASTING THE CONSUMPTION OF FUEL AND ENERGY RESOURCES FOR MILITARY UNITS IN THE ARCTIC ZONE OF THE RUSSIAN FEDERATION

The Russian Arctic is one of the promising economic zones with a rich supply of natural resources. In a world in which territorial divisions, ideological rivalries, ethnic intolerance, and even nuclear proliferation can theoretically be normalized without the use of military force, it is the wealth of energy resources that remains the last casus belli that can lead to catastrophic consequences. That is why the Armed Forces of the Russian Federation are faced with the task of protecting state sovereignty and maintaining security in the Arctic zone. To maintain the combat capability and readiness of a military facility, it is necessary to maintain stocks of fuel and energy resources at the required level. Forecasting the consumption of fuel and energy resources is the most important task. This methodology takes into account factors of various types: periodic (cyclical) and random, including those inherent in military production. All factors affect energy consumption to varying degrees.
 Cyclical factors are the most predictable and have a greater impact on the consumption of fuel and energy resources. Although random factors occupy a small share in the process of energy consumption, the amplitude of deviations can be quite significant.
 The methodology makes it possible to determine the consumption of fuel and energy resources in the context of the increasing complexity of the relationship between the economy and energy and the growing uncertainty of the future development of military units and military bases in the Arctic zone of the Russian Federation based on the applied stochastic differential equation.
 Purpose. Develop a methodology for forecasting the consumption of fuel and energy resources for military units in the Arctic zone of the Russian Federation.
 Methodology in article economic-mathematical methods, and also statistical methods.
 Results: the most informative parameters were obtained, showing some aspects of the process of forecasting the consumption of fuel and energy resources.
 Scope of the results: it is advisable to apply the results obtained in the apartment-operational subdivisions of the logistics management bodies of the military districts to obtain predicted values of the consumption of fuel and energy resources (TER)at military infrastructure facilities (military camps).
 Practical implications it is expedient to apply the received results the economic subjects which are carrying out foreign economic activity, one of which elements are export operations.

Technical and economic assessment of maintenance and repair systems of agricultural machinery

Relevance. The efficiency of agricultural production largely depends on the technical condition of the agricultural machinery fleet. The technical condition, in turn, depends on many factors that determine the level of operation of the equipment. One of the most important factors determining the reliability of agricultural machinery, the cost of restoring and maintaining the working condition of agricultural machinery is the frequency of maintenance. As a result of studies conducted in the agricultural organizations of the region, it was revealed that engineering and technical services, when organizing maintenance and repair (TO and R), use canceled GOST, referring to the fact that domestic equipment, its reliability and performance are not able to recover when frequency of 125 hours. Therefore, the purpose of this study is to determine the effect of the frequency of maintenance and repair on the preservation of the resource and the indicator of the rate of change of the resource, on the performance of the machine-tractor unit (MTA), on fuel consumption, on the costs of restoring and maintaining the working condition of agricultural tractors.Methods. The following methods were used in the study: normative, statistical, expert assessments, experimental, calculation-constructive, economic-mathematical methods. For the economic justification of the periodicity of technical impacts of agricultural machinery, statistical data from agricultural organizations were used, GOST regulating the maintenance and repair of agricultural machinery were used.Results. The maintenance and repair system, regulated by GOST 20793-2009, meets the requirements of technical and production operation of tractors. Traction properties of tractors are higher by 0.7%, specific fuel consumption during agricultural technological operations is lower by 0.5%, labor costs for maintaining and restoring technical readiness are lower by 13.8%.

Definlandization and the new economic policy of Ukraine in the post-war period

Purpose. To investigate the genesis and key historical aspects that have led to the popularization of the concept of “definlandization” in scientific literature, as well as the strategic priorities of the formation of the Marshall Plan within the framework of a possible military and economic union between Great Britain, Ukraine, Poland and the Baltic countries. To propose optimal ways of neutralizing economic threats and to determine probable scenarios of the post-war reconstruction of the infrastructure of the national economy of Ukraine. Methodology. The article uses a combination of correlation and SWOT analysis, which made it possible to calculate the value of natural wealth in the post-war period based on SPSS Data Analysis Software. The used economic-mathematical methods made it possible to form an algorithm for calculating the cost of restoring Ukraine’s total resource losses from Russian aggression in monetary terms and to establish mutually unambiguous correlations with the value of gold using Pearson criterion. Findings. The authors’ spectrum of factors influencing the New Economic Policy in the post-war period has been systemized to determine the estimated amount of necessary resources for the post-war restart of the national economy of Ukraine. For the first time, the need to abandon the Finlandization policy has been scientifically proven, as domestic resources and funds from reparations will not be sufficient for the sustainable development of Ukraine. It was established that the main guarantee of investing in the Ukrainian economy is the high value of natural resources in all regions of Ukraine, which is estimated in monetary terms at approximately 4 trillion hryvnias and the innovative architecture for the “Marshall Plan” of the post-war reconstruction of the infrastructure of Ukraine is given. Originality. The used analytical-mathematical methods made it possible to establish correlations in the regional distribution of the value of natural wealth. In contrast to existing studies, this article not only objectively determined the number of losses in monetary terms but also proposed specific ways of their compensation in the context of the formation of a new economic policy of definlandization of Ukraine on the basis of economic and mathematical modelling of a typical scenario of recovery of the national economy. Practical value. The conducted study on potential ways of definlandization of the national economy was provided for study at the Ukraine Recovery Conference (URC 2022, Lugano, Switzerland). In particular, the authors of the report justified the economic feasibility of moving European production facilities (Robert Bosch GmbH, Siemens, Schneider Electric, SKF, Renault, BMW Group, Mercedes-Benz, Volkswagen, Volvo Group, etc.) from the territory of the Russian Federation, which would facilitate the remigration of Ukrainians and accelerated development of Ukraine based on the principles of decentralization, subsidiarity and definlandization.

Analysis of the probability of crisis events as a determinant of the financial security of food industry enterprises

Analysis of the probability of crisis events as a determinant of the financial security of food industry enterprises

OPTIMIZATION OF LOGISTICS PROCESS MANAGEMENT IN TRADE

The article considers the theoretical and methodological and practical principles of logistics processes management. Current trends in logistics development are outlined. It is shown that the trends demonstrate active implementation in the management processes of the elements of Logistics 4.0. The expediency of using economic-mathematical methods and models to solve logistics tasks is reasoned. An overview of ecommerce processes, typical for today, both in the world and in Ukraine, which directly cause changes in logistics, is made. The problem of optimization of transport costs for delivery of goods from the warehouses of the online store "Hope" to customers, taking into account the non-stationarity (seasonality) factor is defined. The economic-mathematical model of the problem of logistics processes management has been built and adapted as follows: selection of two seasonally-leased warehouses from five reserve ones and optimization of transport costs for delivery of goods from warehouses of the online store to customers. This optimization model was implemented to solve the problem of optimizing logistics costs for the online store "Hope", taking into account seasonal demand, transport tariffs, warehouses capacity and forecasted sales volumes. Various ways to solve the problem of logistics process management, which allows us to show the additional benefits of using these methods and determine the effectiveness of the decision taken are considered as well. The solution for the choice of warehouses and the optimal plan for delivery of goods to customers in order to minimize transportation costs is obtained. It is shown that with the use of economic and mathematical modeling to solve the problem of seasonally adaptive transition for logistics process management, it is possible to make the best choice of two additional leased warehouses from the five reserve ones, to find the optimal delivery plan, to reduce the total length of delivery route and, consequently, the costs of transportation of goods, to avoid shortages of goods in warehouses, in a timely manner and with minimal costs to satisfy the interests of customers of online store "Hope" goods. The economic interpretation of the results of the models implementation is presented and recommendations for their use are provided to achieve minimization of transportation costs, maximum flexibility, speed, reliability of the supply chain, ie to make effective management decisions.

INVESTMENT CLIMATE RESEARCH MODELS OF INDUSTRIAL PARKS OF UKRAINE

The investment climate characterizes the object's attractiveness for a domestic or foreign investor. It is evaluated using various statistical analysis methods, but there has yet to be a universally accepted method of its evaluation now. Therefore, applying economic and mathematical modeling will allow for assessing the relationship between the economic development of regions and their investment climate. The purpose of this research is to apply economic and mathematical tools for the assessment and analysis of the investment climate of industrial parks of Ukraine within specific regions and industries, to forecast the level of capital investments in the regions, as well to evaluate the relationship between the economic development of the region and its investment climate to determine the investment attractiveness of the areas, to diagnose the factors that have the most significant influence on the volume of capital investments and the formation of the investment climate. State clusters were determined and interpreted based on the cluster analysis results. Based on quarterly data, capital investments in the regions were investigated with the trend and seasonal components for certain representatives of clusters and regions. Forecasts were built based on the decomposition models, the level of adequacy of which was confirmed by the indicator of the average percentage absolute error as a high level of reliability. Models for assessing the relationship between the economic development of the region and its investment climate were implemented, and it was determined that the formation of the investment climate, namely the indicator of the volume of capital investment, is most influenced by the volume of exports and retail trade. Three methodological approaches are proposed, such as: assessment of the scale (grouping) of industrial parks; forecast of the level of capital investments in the regions; assessment of the relationship between the economic development of the region and its investment climate to study the investment climate of industrial parks in Ukraine. These methodological approaches will help predict the level of capital investment in the regions where industrial parks are located, as well as assess the relationship between the economic development of the region and its investment climate. The study of economic-mathematical methods and models to evaluate the investment attractiveness of territories, in particular the investment climate, made it possible to create economic-mathematical models of the investment climate of industrial parks of Ukraine, which will allow to determine successful industrial parks, forecast the volume of investments in regions and the factors that most affect the volume capital investment and formation of the investment climate. Economic and mathematical models of the investment climate of industrial parks in Ukraine have been developed. They will allow the development of a strategy for the country's economic activity, contributing to its economic growth. Keywords: economic and mathematical modeling, investment climate, investment attractiveness, industrial park, capital investment, cluster analysis, trend equation, forecast.

Economic assessment of dynamics of energy consumption by production units of the enterprise

Methods. The study of energy consumption dynamics is based on the methods of spectral analysis. The economic evaluation of the results of the implementation of energy saving measures was carried out using the method of economic analysis. The method of economic-mathematical modeling was applied when creating a cost model for the dynamic component of electricity consumed by the enterprise. Results. It was established that the spectral analysis of the active power consumed by the enterprise allows to estimate the saving of electricity and the economic efficiency of energy-saving measures by improving the dynamics of energy consumption. It is proposed to form a fund for the economic stimulation of energy saving due to the improvement of consumption dynamics and to distribute it among the main workshops of the enterprise by means of a frequency analysis of the dynamics of energy consumption by the production units of the enterprise. An economic-mathematical model of costs for the dynamic component of electricity consumed by the enterprise and its main technological divisions has been developed, which allows to calculate and distribute the fund for material stimulation of the dynamics of energy consumption between the main technological divisions of the enterprise. Spectral analysis of the active power consumed by the enterprise allows to assess not only the economic efficiency of energy saving measures, but also the losses in case of their non-fulfillment, which allows to impose fines on the personnel of the relevant units of the enterprise. Novelty. For the first time, an economic-mathematical method for diagnosing the effectiveness of energy-saving measures by individual units of the enterprise was developed based on spectral analysis and economic assessment of energy consumption dynamics. Practical value. The developed method of forming a fund of financial incentives for the company's personnel for the effective implementation of measures to improve the dynamics of energy consumption allows taking into account the contribution of the company's divisions to the overall saving of electricity.

Економіко-математичне моделювання оптимізації виробничих витрат у садівництві

Goal. To build an economic-mathematical model of optimizing the structure of production costs and to reveal the relationship between the investigated indicators and the factors that influence their value. Methods. Scientific abstractions — for the formation of theoretical generalizations and conclusions; the economic-mathematical method — to optimize the cost structure in horticulture; the method of system analysis and synthesis — to establish cause-and-effect relationships in the formation of production costs in horticulture. Results. To improve the management of expenses in the direction of their optimization, it is advisable to use the method of optimization modeling for various structures of apple plantations. The analysis of the simulation results indicates the possibility of reducing the cost of growing apples under the condition of rational distribution of costs. A comparison of the actual indicators of financing apple cultivation with those obtained in the modeling process shows the need for a reasonable approach to spending money on mineral and organic fertilizers, means of protection, and wages. It is these cost items that are the most important in shaping the yield of apples according to the correlation-regression analysis and the data obtained during the calculation of the economic-mathematical model of cost optimization. From the equation obtained as a result of conducting such an analysis, it follows that the listed factors should be placed in the following order according to the degree of importance: depreciation of agricultural machinery, other direct costs, costs of organic fertilizers and mineral fertilizers, fuel and lubricants, general production costs, costs of protective equipment, depreciation of perennial plantings, labor costs. Using the results of cost optimization modeling, it is quite possible not only to increase the yield of apples by 11.88–28.81% but also to reduce their cost price and to reduce total costs by 6.3–67.7%. Conclusions. Optimizing the cost structure using the methods of economic-mathematical modeling is one of the ways to effectively manage funds. The optimal cost structure justified for the horticulture industry makes it possible to reduce the cost price and increase the yield of apples.

ОСОБЛИВОСТІ СТРАТЕГІЧНОГО ПЛАНУВАННЯ ПРОМИСЛОВИХ ПІДПРИЄМСТВ ЗА УМОВ ЄВРОІНТЕГРАЦІЇ

The approaches of economist scientists to the definition of strategic planning of the enterprise, its purpose and goals to ensure the development of financial and economic activity have been studied. The main criteria that should be taken into account in order to successfully organize strategic planning processes at an industrial enterprise are substantiated. The effectiveness of strategic planning at an industrial enterprise depends on the formation of strategic plans, therefore it is necessary for managers to clearly define their principles. The basic principles of the formation of strategic plans of industrial enterprises under the conditions of European integration, on which the effectiveness of strategic planning depends, are determined. The main directions of changes to the approaches to the strategic planning of enterprises in the conditions of the strengthening of the European integration processes are revealed. Modern methods of strategic planning are characterized, which are the basis for the formation of forecast indicators, plans, projects and strategies for the development of the enterprise. For the successful implementation of the development strategy of an industrial enterprise, it is important to choose strategic planning methods that would provide an opportunity to form an information and analytical base regarding forecast indicators, strategic plans and projects. Strategic planning methods that can be used by enterprises include: socio-economic analysis methods, direct engineering and economic calculations, economic-mathematical methods, balance method, expert methods and methods of system analysis and synthesis. It was concluded that the management staff, based on the features, capabilities and characteristics of the enterprise, chooses its own approach to the organization of strategic planning based on well-founded principles and models. Because of that, the strategic planning models that domestic industrial enterprises choose in practice are given. In the strategic management of an industrial enterprise, it is worth distinguishing approaches to strategic and long-term planning, because in the context of factor characteristics, they have a number of differences. Effective strategic management of industrial enterprises involves the study of both resource and financial opportunities and the overall potential of the enterprise. In the context of the strategic development of the enterprise, capacity building is based on the study and coordination of factors of both the internal and external environment. A number of tasks regarding the improvement of strategic planning at industrial enterprises in the current conditions of operation are singled out.

ОЦІНКА ІНВЕСТИЦІЙНОЇ ПРИВАБЛИВОСТІ СФЕРИ ТУРИЗМУ СТАТИСТИЧНИМИ ТА МАТЕМАТИЧНИМИ МЕТОДАМИ

The purpose of the article is to conduct an analysis of the investment attractiveness of tourism industry sectors for planning the process of sustainable development of tourism and hospitality industry enterprises. Recovery of Ukraine's economy after the war is impossible without the development of the tourism industry. Affected by Russian military aggression and the global pandemic, the tourism industry will feel a great need for investment income for sustainable development. A detailed scientific analysis of the enterprise's economic activity is necessary for the effectiveness of the investment project. The evaluation of indicators of the attractiveness of investments in the tourism industry was carried out using statistical and economic-mathematical methods on the basis of financial indicators of the activities of tourism enterprises using the concept of the optimal portfolio of investments, initiated by H. Markovits. According to the results of the financial performance indicators of tourism enterprises for 2016-2019, the coefficients of investment attractiveness of various sectors were found, namely the profitability and risk of capital investments in the enterprise. Solving the problem of quadratic programming using the SOLVER package based on MS EXCEL spreadsheets made it possible to identify the most attractive sectors of the tourism industry, that is, those with a higher rate of return and a low level of riskiness of capital investments. Among the tourism business enterprises, these were "activities of travel agencies", as well as "provision of other booking services and related activities". Studies have shown that certain tourism industries are closely correlated in their cooperation, which is quite understandable. A promising direction of further development of the raised topic is the development of methods of practical application of the obtained results for carrying out investment activities in the real sector of the tourism industry for the restoration of sustainable financial and economic development of economic entities in the post-war period.

Modeling Scenarios of Adaptation of Regional Socio-Ecological and Economic Systems to Global Climate Change

The relevance of the study is due to the fact that in recent decades a socio-economic development of the territories of states and regions has been significantly affected by global climate change. Due to changes in temperature, precipitation, solar radiation, etc. fires are occurring; individual ecosystems are being transformed, which in turn negatively affects the quality of life of the population as well as the development of industries and economic systems. All of the above, on the one hand, emphasizes the relevance of developing tools and models for assessing the consequences of such an impact, and, on the other hand, highlights the need to develop a special adaptive mechanism for managing the socio-ecological and economic system, taking into account the impact of climate change. Accordingly, the aim of the work was to develop a model for the implementation of scenarios and forecasting the consequences of global climate change for regional socio-ecological and economic systems. To achieve this goal, the authors put forward a hypothesis about the possibility of developing and constructing an instrumental numerical model that allows, based on long-term statistical data, for modeling scenarios of adaptation of multi-level (both global and regional) socio-ecological and economic systems to the consequences of global climate change. To achieve this goal, a set of general scientific and economic-mathematical methods was used, mutually complementing each other, including methods of abstract-logical analysis, principal component analysis (PCA), methods of system dynamics, etc. The authors obtained the following results: firstly, an analytical model of adaptive development of the regional socio-ecological-economic system was developed; secondly, a list of basic prerequisites that have a fundamental impact on this system due to climate change was substantiated; thirdly, a forecast model was proposed of a stable trajectory of the development of a regional socio-ecological-economic system under the conditions of global climate change. The scientific significance of the study is to expand scientific knowledge about approaches to modeling scenarios for adaptation of socio-ecological-economic systems to global climate change. The practical significance of the work consists in the possibility of using the results for the development and improvement of plans for the adaptation of Russia's regions to climate change, including in the areas of environmental management and economic activity, civil defense, protection of the population and territories from natural and man-made emergencies.

FORMATION OF AN EFFECTIVE MANAGEMENT INFORMATION SUPPORT SYSTEM

The introduction of modern economic market relations in Ukraine has set society many important tasks, one of which is the search for new forms and methods of managing the production and sale of goods or services. Under these conditions, a complex, systematic approach to solving this or that economic problem becomes especially important. When developing a complex system of management of economic activity, it is advisable to use the experience of the organization of management, accumulated both in our country and abroad. In this regard, new information technologies based on the use of computer technology, distributed (decentralized) information processing, and economic-mathematical methods are of particular interest. Today, we are witnessing the global transformation of the entire earthly civilization - the transition from an industrial society to an information society. Until now, there is no clearly defined concept of optimal information provision of enterprises, the end product of which is the provision of services and the performance of certain tasks, that is, an intangible type of product. Therefore, the development of a defined system of information support of management bodies should be preceded by a deep analysis of both the economic activity of such an enterprise and the existing situation with information support. The scientific article describes the approaches of using MC Project and other modern programs for evaluating the effectiveness of business processes. It was found that Microsoft Project Standard is the main tool for project management, including for planning and forming project execution schedules. In combination with the Microsoft Project Server server, it allows you to organize collective work on the project in the scope of one working group. The availability of powerful tools makes it possible to flexibly adapt programs to automatically perform mass calculations, which depend both on the specifics of a specific area of accounting and on the peculiarities of the accounting policy of the enterprise. At the same time, the specified tools not only allow changing individual parameters, such as, for example, codes of accounts, subaccounts, analytical accounts, their names, tax rates, etc., but also allow you to describe and modify the rules for performing calculations quite completely. Proposed ways of improving the information support of management activities, which will allow to reveal its external and internal features and formation and use, determine its characteristics, which will allow to increase the efficiency of information support of management activities.

Development and approbation of a software solution for the investment portfolios formation using fractal analysis and predictive models

This paper describes the development and approbation of the software solution, which implements the methodology of forming recommendations for the composition of investment portfolios using fractal analysis and long memory predictive models, which is the result of research conducted over several years at the Department of Information Systems and Mathematical Methods in Economics of PSU. The general algorithm of the program includes four main steps: 1) obtaining and preparing data; 2) sorting assets by the fractal dimension of their price series; 3) forecasting asset returns; 4) forming portfolios (determining asset shares). The described algorithm stages correspond to the structure of the program solution, expressed by the set of its subsystems. The features of the developed program are as follows: possibility to load data of share prices from the FINAM website; calculation of the fractal dimension of asset price series by the DFA and minimum coverage methods; asset returns forecasting using the ARFIMA and ARFIMA-GARCH models; selection of portfolio structures based both on the forecasted and historical data; possibility of multiple generation of portfolios based on random-selected assets with characteristics averaging; evaluation of portfolio characteristics using test data (if any); support for multi-core processors for multiple acceleration of calculations; windowed graphical interface. The results of program approbation on the Russian stock market data under crisis economic conditions are given. On the whole, these results are in line with those obtained earlier on the developed US market data. The developed program can be used by portfolio investors, carrying out investment activities in the international financial markets. Scientific application of the program is important: its users can be scientists, students and other researchers of innovative methods of investment portfolios formation.

თანამედროვე მონეტარული თეორიის შესახებ

თანამედროვე მონეტარული თეორიის შესახებ

Scientific Research and Recent Findings in Financial Monitoring

The article discusses the existing studies on the issue of financial monitoring and the suggestions that their authors have. The discussion of these studies begins with the American scientist Edward Altman's Z-model, which he proposed to predict the risk of bankruptcy for companies. The article presents both an earlier and a modified version of the Z-model developed by Edward Altman. The article also discusses and evaluates the 9-factor model developed by V. Fulmer and R. Saifulin and G. Kadikov's four-factor models. Among the more recent studies in the field of monitoring is the study of the Portuguese scientist Ana Paula Lopez, who found that the companies served by the audiences of the "big four" no longer cheat in the financial part. Malaysian scholars Noor Aisha Nizan and Zuhaikha Zailan found in 2019 that it is best to combine financial audits with technological and human audits. Also, in 2019, Vilnius scientist P. Poshinaus argued that monitoring should be carried out only by economic-mathematical methods, because they provide great opportunities for finding financial irregularities. And in 2020, Czech scientist Aneta Zemankova proposed to the public to use artificial intelligence in monitoring. With its implementation, smart audit procedures and smart contracts can be performed in an automated manner. The authors of the article conclude that the auditors of Georgia, due to the low level of mathematical education, cannot use blockchains and artificial intelligence, but also economic-mathematical models in the audit, and raise the issue of the need to retrain them in this direction. The article discusses the issues of dividing diversified companies into responsibility centers and their financial monitoring. Keywords: Financial monitoring; probability of bankruptcy; Z - model; Fulmer's model; mathematical models; Responsible centers.

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.

Развитие инструментария оценки процесса реализации программ диверсификации производства продукции на предприятиях оборонно-промышленного комплекса

The article presents the results of a study, the relevance of which is determined by the urgent need to increase the optimality of the process of diversification of production in the branches of the military-industrial complex. The subject of the study is the tools for assessing the process of implementing sectoral programs of this diversification in the conditions of uncertainty of the external environment of enterprises and incompleteness of initial data during the anti-Russian hybrid war. The subject of the study is the tools for assessing the process of implementing sectoral programs of this diversification in the conditions of uncertainty of the external environment of enterprises and incompleteness of initial data during the anti-Russian hybrid war. Expert and economic-mathematical methods were used in their development. The application of the proposed models in practice helps to optimize the diversification of production at enterprises of the branches of the military-industrial complex.

Мультипликативные экономические эффекты в арктических рыбохозяйственных проектах

The work is focused on studying the possibilities and assessing the prospects for creating fish-breeding enterprises in the Russian Arctic, taking into account the existing and planned infrastructure provision. The authors presented and tested the methodology for assessing the multiplicative effects on the example of a fish-breeding enterprise in the city of Pevek. The methodology is based on simulation modeling and scenario approach. Consideration of the place of bioresources in the Arctic aquatic production complexes with the usage of economic-mathematical evaluation methods was performed for the first time. The authors prove that the fish-breeding project of the Chukot Autonomous District has acceptable indicators of economic efficiency, as well as a fairly significant social potency, while the main volume of multiplicative effects is localized at the regional level. The estimates obtained can be useful when making decisions regarding the development of aquaculture in the Arctic zone of the Russian Federation, as well as determining the spatial configuration of centers of economic activity in this region.