ru / en # 08.00.13 Mathematical and instrumental methods of Economics

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The article presents the results of a study of higher education institutions in the Krasnodar region based on the use of an integrated approach, identifies priority aspects of the development of universities. The level of the educational institution was calculated taking into account educational, research and international activities, staff and infrastructure. Information about the level of assessment of educational institutions is used by university applicants when they choose a particular institution. The work was carried out on the basis of monitoring the performance of educational institutions of higher education in the Krasnodar region in 2018. During the integral assessment, standardization methods were used to compare the indicator with the reference and linear transformations, as well as the method of additive convolution and the method of calculating distances. The studies showed the level of each institution of higher education, the ways of their development are highlighted. Thus, the assessment of higher education institutions, carried out on the basis of an integral indicator, covers almost all aspects of educational institutions, it allows you to quickly and objectively get an idea of universities, identify weaknesses and strengths, the results of the development of the main components of higher education institutions, and identify the reserves necessary to ensure its sustainable and effective development
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In 1979, non-numerical data statistics was singled out as an independent area of applied statistics. Initially, the term "statistics of objects of non-numerical nature" was used to denote this area of mathematical methods of economics. Our basic non-numeric statistics textbook is called "Non-Numeric Statistics". Non-numerical data statistics is one of the four main areas of applied statistics (along with number statistics, multidimensional statistical analysis, statistics of time series and random processes). Statistics of non-numerical data are divided into statistics in spaces of a general nature and sections devoted to specific types of non-numerical data (statistics of interval data, statistics of fuzzy sets, statistics of binary relations, etc.). Currently, statistics in spaces of a general nature is the central part of applied statistics, and non-numeric data statistics including it is the main area of applied statistics. This statement is confirmed, in particular, by the analysis of publications in the section "Mathematical Research Methods" of the journal "Industrial Laboratory. Diagnostics of Materials" - the main place of publication of russian studies on applied statistics. This article is devoted to the analysis of the basic ideas of non-numerical data statistics against the background of the development of applied statistics from the perspective of a new paradigm of mathematical research methods. Various types of non-numeric data are described. The historical path of statistical science is analyzed. We have discussed the development of statistics of non-numerical data. The article analyzes basic ideas of statistics in spaces of a general nature: average values, laws of large numbers, extreme statistical problems, nonparametric estimates of the probability density, classification methods (diagnostics and cluster analysis), statistics of the integral type. Some statistical methods for analyzing data lying in specific spaces of non-numeric nature are briefly considered: non-parametric statistics (real distributions usually differ significantly from normal), statistics of fuzzy sets, theory of expert estimates (the Kemeny median is a sample average of expert orderings), etc. We have also discussed some unsolved problems in statistics of nonnumeric data
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The article considers an approach to managing the production process in agriculture based on modeling and evaluation of added value chains. The work has proposed a scheme of links for the production chain of added value creation that contains source control and financing cash flow which comes first in the link of agricultural production, then produced products are supplied to the accumulator, and from there it sequentially passes through the links of the value chain of the cyclic processing facilities, from which finished products are marketed and the resulting revenue is directed to the source of funding and management. We have given mathematical descriptions of the movement of financial and material flows in the links of the developed value chain, and mathematical models for calculating the volume of material and financial flows are proposed. Financial flows were also investigated to compensate for the cost of converting material flows and their mathematical descriptions. The article obtains a mathematical model of the economic efficiency of the production process and proposes a mathematical model for calculating the minimum price for socially significant processing products
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One of the key problems facing the credit institution is the late payment of the loan. Firstly, it is a deeper analysis - in order to be carried out “manually” it is not even required several days, but weeks. Secondly, it allows you to work with clients much faster. And most importantly scoring allows you to negate the influence of the human factor. An automated system, no matter how you look, cannot be liked or not. Data analysis is only based on facts. Scoring is beneficial to all. The bank is able to work faster and reduce the risk of loan defaults. Clients, in turn, can apply for a loan on terms that are more favorable
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This article is devoted to rating assessment of the socio-economic situation of the Krasnodar region, presented by such agencies as "RAEKS-Analytics", "Expert RA" and "National Rating Agency". The methodologies used by these agencies were studied and analyzed. A comparison of these methodologies was also conducted. As a result, a number of their shortcomings were identified, including the lack of a complete methodological model in the public domain. Some agencies do not provide links to statistics that are used in the analysis. In the article using the STATISTICA environment, a statistical analysis of data reflecting the level of socio-economic situation of the Krasnodar region is carried out. Based on the work , the article created a discriminant model for assessing the socio-economic development of urban districts of the Krasnodar region with a confidence of 85%. The study conducted a cluster, discriminant, classification (decision trees), coefficient (proposed by the authors) based on the data of the Federal State Statistics website for the period from 2009 to 2018 in the city districts: Krasnodar, Anapa, Armavir, Gelendzhik, Goryachiy Klyuch, Novorossiysk Sochi. During the study, analyzes such as cluster and classification trees showed poor results, since they are not able to detect latent nonlinear relationships between the study indicators. Using the constructed discriminant model, we have carried out an analysis of the socio-economic development of urban districts of the Krasnodar region for the period 2009-2018, which allows us to identify the leaders and the outsiders
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Dynamic programming is designed to solve discrete optimal control problems. According to this method, the optimal solution in a multidimensional problem is found by decomposing it into stages, each of which represents a subproblem with respect to one variable. In economic problems, the number of stages is the planning horizon. The choice of a planning horizon is necessary for a rigorous statement of the applied problem in the field of economics and management, but it is often difficult to justify. We see a way out in the use of asymptotically optimal plans for which the values of the optimization criterion differ little from its values for optimal plans for all sufficiently large planning horizons. The main result of the paper is the existence of an asymptotically optimal plan. The proof is carried out in several statements. If the sum of the maximums of the transition functions tends to 0, the existence of an asymptotically optimal plan is obtained in Theorem 1. A special case is models with a discount at a discount coefficient less than 1. The main part of the article is devoted to models with a discount coefficient equal to 1. Theorem 2 on the highway is proved for base set of a finite number of elements. In Theorem 3, a statement is obtained on the approximation of an arbitrary set by a finite one. In the final Theorem 4, the existence of an asymptotically optimal plan is proved in the general case. The term “magistral” is associated with a well-known recommendation to drivers: in order to get from point A to point B, it is advisable to go to the highway (magistral) at the initial section of the road, and then exit the highway and get to point B. The recommendation for choosing the optimal one is similar trajectories using the Pontryagin maximum principle in the model of the optimal distribution of time between obtaining knowledge and developing skills. This fact underlines the methodological proximity of dynamic programming and the Pontryagin maximum principle
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To assess the impact of investments on the results of the Agro-industrial complex, we use an adaptive management system for open systems
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The instrumental methods of economics include the Monte Carlo method (statistical simulations method). It is widely used in the development, study and application of mathematical research methods in econometrics, applied statistics, organizational and economic modeling, in the development and making management decisions, in the basis of simulation modeling. The new paradigm of mathematical research methods developed by us is based on the use of the Monte Carlo method. In mathematical statistics, limit theorems on the asymptotic behavior of the considered random values were obtained for many methods of data analysis with an unlimited increase in sample volumes. The next step is to study the properties of these random values for finite sample sizes. For such a study, the Monte-Carlo method is used. In this article, we use this method to study the properties of statistical criteria for testing the homogeneity of two independent samples. We considered the most used in the analysis of real data criteria - Cramer-Welch, which coincides with the equality of the sample sizes with Student's criterion; Lord, Wilcoxon (Mann-Whitney), Wolfowitz, Van der Waerden, Smirnov, type omega-square (Lehmann-Rosenblatt). The Monte Carlo method allows us to estimate the rates of convergence of distributions of criteria statistics to the limits, to compare the properties of the criteria for finite sample sizes. To use the Monte Carlo method, it is necessary to select the distribution functions of the elements of the two samples. For this purpose, normal and Weibull – Gnedenko distributions are used. The recommendation was received: to test the hypothesis of coincidence of distribution functions of two samples, it is advisable to use the Lehmann-Rosenblatt (type omega-square) test. If there is reason to assume that the distributions differ mainly by the shift, then the Wilcoxon test and Van der Waerden criteria can also be used. However, even in this case, the omega-square type test may be more powerful. In the general case, besides the Lehmann-Rosenblatt criterion, the use of the Smirnov criterion is permissible, although for this criterion the real level of significance may differ from the nominal level of significance. We sstudied the frequency of discrepancies of statistical findings on different criteria
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This article is devoted to a problem of effective management of a financial and economic condition of companies on the example of the enterprises of oil products supply. We consider questions of support of adoption of management decisions which concern stabilization of a financial condition of the company and as a result of decrease in financial risks. The article also provides a description of the program complex called FESP_ON developed by the authors allowing to carry out the profound complex assessment of a financial and economic condition of Societies of oil products supply
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In their previous works, the authors solved the problem of cognitive-target structuring and formalization of the subject area, as well as the synthesis and verification of statistical and system-cognitive models. This work is devoted to the application of these models to solve the problem of forecasting the impact of the volume and direction of investment in agriculture on the economic component of the quality of life of the population of the region. This work is devoted to the use of previously created and verified models to solve the problem of decision-making on the volume and direction of investment in agriculture, improving the quality of life of the population of the region