08.00.13 Mathematical and instrumental methods of Economics
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BASIC REQUIREMENTS FOR DATA ANALYSIS METHODS (ON THE EXAMPLE OF CLASSIFICATION TASKS)
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThere is a need to clean up the classification methods. This will increase their role in solving applied problems, in particular, in the diagnosis of materials. For this, first of all, it is necessary to develop requirements that classification methods must satisfy. The initial formulation of such requirements is the main content of this work. Mathematical classification methods are considered as part of the applied statistics methods. The natural requirements to the considered methods of data analysis and the presentation of calculation results arising from the achievements and ideas accumulated by the national probabilistic and statistical scientific school are discussed. Concrete recommendations are given on a number of issues, as well as criticism of individual errors. In particular, data analysis methods must be invariant with respect to the permissible transformations of the scales in which the data are measured, i.e. methods should be adequate in the sense of measurement theory. The basis of a specific statistical method of data analysis is always one or another probabilistic model. It should be clearly described, its premises justified - either from theoretical considerations, or experimentally. Data processing methods intended for use in real-world problems should be investigated for stability with respect to the tolerances of the initial data and model premises. The accuracy of the solutions given by the method used should be indicated. When publishing the results of statistical analysis of real data, it is necessary to indicate their accuracy (confidence intervals). As an estimate of the predictive power of the classification algorithm, it is recommended to use predictive power instead of the proportion of correct forecasts. Mathematical research methods are divided into "exploratory analysis" and "evidence-based statistics." Specific requirements for data processing methods arise in connection with their "docking" during sequential execution. The article discusses limits of applicability of probabilistic-statistical methods. Concrete statements of classification problems and typical errors when applying various methods for solving them are also considered
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08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article discusses the use of machine learning methods and fuzzy production systems for studying the social and economic development of urban districts, areas and settlements of the Krasnodar region. The fundamental patterns and their connection with quantitative and qualitative indicators are considered
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CHARACTERIZATION OF MODELS WITH DISCOUNTING
08.00.13 Mathematical and instrumental methods of Economics
DescriptionAmong the widely used economic-mathematical models, dynamic programming plays an important role, and among them, models with discounting. The most famous example is the model for calculating the net present value (NPV) as an estimate of the efficiency of the investment project. In the article, it is clarified which features are distinguished by models with discounting among all models of dynamic programming. In models with discounting, the comparison of plans does not change when the time of the beginning of the implementation of plans changes, ie. there is a stability of the results of comparing plans. It is proved that if the results of comparing plans for 1 and 2 steps are stable in the dynamic programming model, then this model is a model with discounting. This theorem shows that the introduction of discounted functions for the estimation of the effect is justified only in stable economic conditions in which the orderliness of managerial decisions does not change from year to year. In other words, if at the beginning of the period under consideration the first solution is better than the second, then at all other times, up to the end of the period under consideration, the first solution is better than the second. Stable economic conditions are rarely found in the modern economy with its constant changes, including those caused by innovations. Therefore, the decision to choose (to implement) an investment project from a set of possible ones can not be based solely on the calculation of discounted project performance indicators, such as net present value and internal rate of return. Such indicators can only play a supporting role. Decide on the choice of an investment project for implementation is necessary on the basis of the whole range of social, technological, environmental, economic, political factors
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STRATEGIC PLANNING AND MANAGEMENT OF A HOLDING BASED ON INFORMATION AND COGNITIVE TECHNOLOGIES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn the article, we develop the methodology of strategic planning and management of a holding, on the theoretical basis of automated system-cognitive analysis (ASC-analysis). This methodology provides scientific research of any holding by creating and researching its model. The methodology includes both the synthesis, adaptation and verification of system-cognitive models of the holding, and the use of these models for strategic planning and decision support for the management of the holding, as a complex, multiparametric, nonlinear system. The relevance of the research is due to the special role of holdings and other corporate integrated structures both in Russia as a whole and, in particular, in the Krasnodar region. Despite obvious system advantages, holdings face a wide range of problems related to management efficiency, ensuring their sustainable functioning, etc. The proposed methodology offers ways to solve these problems and can be successfully applied in holdings and other corporate integrated structures of various regions, volumes and areas of activity, which determines the relevance of the research topic. The level of significance and scientific novelty of the Research consists in the development of conceptual and theoretical and methodological provisions aimed at managing the development of holdings. The expected results and their significance are that the methodology developed as a result of the Research can be applied by holding companies and other corporate integrated structures and will significantly improve the quality of their management
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PROBABILITY-STATISTICAL MODELS OF CORRELATION AND REGRESSION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe correlation and determination coefficients are widely used in statistical data analysis. According to measurement theory, Pearson's linear paired correlation coefficient is applicable to variables measured on an interval scale. It cannot be used in the analysis of ordinal data. The nonparametric Spearman and Kendall rank coefficients estimate the relationship of ordinal variables. The critical value when testing the significance of the difference of the correlation coefficient from 0 depends on the sample size. Therefore, using the Chaddock Scale is incorrect. When using a passive experiment, the correlation coefficients are reasonably used for prediction, but not for control. To obtain probabilistic-statistical models intended for control, an active experiment is required. The effect of outliers on the Pearson correlation coefficient is very large. With an increase in the number of analyzed sets of predictors, the maximum of the corresponding correlation coefficients — indicators of approximation quality noticeably increases (the effect of “inflation” of the correlation coefficient). Four main regression analysis models are considered. Models of the least squares method with a determinate independent variable are distinguished. The distribution of deviations is arbitrary, however, to obtain the limit distributions of parameter estimates and regression dependences, we assume that the conditions of the central limit theorem are satisfied. The second type of model is based on a sample of random vectors. The dependence is nonparametric, the distribution of the two-dimensional vector is arbitrary. The estimation of the variance of an independent variable can be discussed only in the model based on a sample of random vectors, as well as the determination coefficient as a quality criterion for the model. Time series smoothing is discussed. Methods of restoring dependencies in spaces of a general nature are considered. It is shown that the limiting distribution of the natural estimate of the dimensionality of the model is geometric, and the construction of an informative subset of features encounters the effect of "inflation coefficient correlation". Various approaches to the regression analysis of interval data are discussed. Analysis of the variety of regression analysis models leads to the conclusion that there is no single “standard model”
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08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe article provides a comparative analysis of assessments of the socio-economic development of the Krasnodar region from such well-known rating agencies as Standard & Poors, Moody’s, Fitch Ratings, which belong to the United States of America. The studied ratings are compared with the ratings of the national agency of the Russian Federation called “Expert RA”. The values of the established ratings are examined, as well as number of possible reasons why the ratings of the United States of America differ from the ratings of the Russian Federation, for example, economic and political reasons, and, subsequently, how these ratings affect the investment attractiveness of the Krasnodar region. The article explains positive and negative aspects of the integrated methodology used by international rating agencies, consisting of software and expert opinion, the level of access to it for study and analysis. We study another (local) source of information on the investment attractiveness of the Krasnodar region, which is a state institution, namely the Department of Investments and Development of Small and Medium Enterprises of the Krasnodar region. Options are proposed for improving the system of analysis of statistical data through methods that are based on a clear mathematical approach to provide an adequate assessment of the region and municipalities without the influence of subjective expert opinion
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08.00.13 Mathematical and instrumental methods of Economics
DescriptionWe use an adaptive management system for open systems to assess the impact of investments on the results of the Agro-industrial complex
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08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn previous works, the authors solved the problem of cognitive structuring and formalization of the subject area, synthesis and verification of system-cognitive models, predicting the impact of nomenclature and sales volumes on the profit and profitability of the trading company, decision support for the selection of such nomenclature and sales volumes, which cause a given target profit and profitability of the company. This work is devoted to the study of the simulated subject area by studying its SC-model
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SCORING SYSTEM BASED ON INFORMATION-COGNITIVE MODELING
08.00.13 Mathematical and instrumental methods of Economics
DescriptionOne 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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EXISTENCE OF ASYMPTOTICALLY OPTIMAL PLANS IN DISCRETE PROBLEMS OF DYNAMIC PROGRAMMING
08.00.13 Mathematical and instrumental methods of Economics
DescriptionDynamic 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