The article develops economic and mathematical models as a tool for conducting factor financial analysis of the prospects for the development of an industrial enterprise. The functioning of the developed economic and mathematical models is based on the DuPont model, which allows analyzing the dynamics of the company’s profitability in the course of two-factor and three-factor financial analysis. The proposed model tools are based on the convergence of deterministic financial analysis methods embedded in the DuPont model and simulation methods that allow analysis under the influence of random factors. The constructed economic and mathematical models for forecasting profitability use the company’s retrospective data on its financial condition: the amount of profit, revenue, assets, and equity. The constructed simulation models are implemented in the OMEGA software product and included in the computer technology for predicting the profitability of an industrial enterprise. The architecture of the proposed tools is presented, and the results of simulation experiments performed on models are demonstrated.

The article discusses the issues of financial stability of enterprises in unstable economic conditions. The authors propose a formal model of the gradual quantitative assessment of the financial stability of enterprises based on the use of regression equations with determination coefficients. The financial stability of enterprises is described by the indicators of their financial status according to the regional-average and industry-average levels. A qualitative assessment of the financial stability potential of enterprises is given based on the interpretation of deviations of the financial stability coefficients. The article defines the limiting values of financial stability of enterprises, the output of which allows the unambiguous interpretation of this concept and its level. An example that determines the financial stability of various Russian enterprises is also presented.

In the oil and gas industry, which is the basis of the Russian energy market, a significant and urgent question arises: How to distribute companies according to their investment attractiveness? Accordingly, quantitative indicators are needed. Lacking extensive experience in the practical implementation of fundamental rating tools, work is needed to develop methodologies of weighting coefficients and lists, built on the experience of the “big three” rating agencies. The article proposes an algorithm for forming an integral rating of companies based on financial reporting indicators and the author’s rules of fuzzy logic based on the principle of “circular convolution”, from the best to the slave, deepening the analysis to the center, when all companies are exhausted and places in the rating are distributed. The problem of assessing and integrally indexing the indicators of large companies in leading sectors of the economy (e.g., oil and gas, banks, electricity) is becoming manifest, while it is obvious that there is competition between large companies of the country’s leading industries for state investment resources. The nature of the leading industries is such that it is necessary to assess the quality of the company’s functioning based on the formation of rating groups. Based on the rating, investments are distributed among the companies under consideration. The author has developed a portfolio model that is analogous to the Harry Max Markowitz model, which does not contradict this model but allows consideration of a broader range of risk assessments used in the model (for example, the rating of companies). The optimal portfolio is built, taking into account the resulting index and the initial grouping in the hierarchical data correction mode. The logically sequential method of circular convolution of four important indicators to an integral index and a mathematically substantiated method for optimizing the minimax portfolio presented in the work will allow the investor to develop optimal (from the point of view of the transparency of the apparatus used, mathematical feasibility and time spent on the implementation of the software package) tools for investing and enlarging his capital.

The article assesses the main functional elements of public Finance management: planning, operational management and control. Financial planning and forecasting presently depend not only on macroeconomic and microeconomic factors, but also on geopolitical factors. Economic sanctions, which are still ongoing, have a particular impact, so it is impossible to make an accurate forecast in the management of public finances. Operational public financial management can never be considered without public resources designed to support and implement the activities of all areas of the country’s life. The paper pays special attention to the control function due to the lack of a single objective control system. To improve efficiency, the authors propose to use certain criteria: the performance criterion and the criterion of inappropriate use of budget funds. The paper calculates the dependence of Federal budget revenues on the level of gross domestic product (GDP) and the level of unemployment. The authors use for the calculation a standard form of regression equation that takes into account statistical correlations. The results of this study can be used to improve the efficiency of Federal budget revenue planning.

Agriculture faces a series of challenges, i.e. guaranteeing national food security, increasing farmer’s income and reducing the adverse effects on environment and human health associated with the use of fertilizers and biocides. At the same time, the availability of resources (e.g. agricultural land) decreases. The objective of this study in this article is to operationalize a methodology to assess the effectiveness of new crop and livestock technologies in attaining rural development goals. Cropping systems, quantified in terms of inputs and outputs, are used as the smallest unit of analysis in this study. A land use model, based on linear programming techniques, is used to assess the contribution of alternative cropping systems to rural development goals. Results of this study contribute to the formulation of agricultural policies and a research agenda aiming at stimulating rural development.

The stage of the crisis in the use of energy resources is the main aspect of the development of an economic model for the rational use of energy resources. The scientific approach of rational economic development to develop regression models of energy conservation is necessary for economic growth and is associated with ecosystem and climate change, these are the reasons for reducing resource use. The modern energy scenario from a global point of view should include regression models for optimizing the main renewable energy sources. The components of such energy management models should reduce costs and include environmental benefits. New energy sources are the baseline for our regression model. New and renewable energy sources include geothermal, wind, solar and others. The main role in the development of such models is played by the possibility of introducing an ecological balance, as well as calculations for the optimization and rational use of renewable energy sources using natural resources.