The article presents a model based on the calculations of optimal size of the investment portfolio for a non-state pension fund (NPF). There are risks associated with the functioning of NPFs and their seemingly non-profit organization status. The primary risk in this regard is related to attracting solvent enough participants which will ensure future payouts. To achieve our research goals, we used the elements of data mining results technology, more specifically, the MARSPline module in the Statistica application package. This program allows constructing a regression model in multidimensional space as well as a spline surface depending on income payments to the pension fund and investment incomes and expenses from retirement assets. The resulting regression model has established the connections between the variables with a rather precise approximation. It can be applied not only to NPF activities, but also with insurance organizations and other financial intermediaries. Purpose. The purpose of this study is to build an economic and mathematical model for the formation of an investment portfolio in the NPF. This portfolio minimizes initial
<p class="TtuloAbstract">The aim of the article is to study the issues of analysis, modeling with the purpose of forecasting the payment of value added tax (VAT) on goods, works and services imported as imports into the customs territory of Ukraine. The reliability and validity of the planned VAT rate depend on the assessment of the status, forecast, seasonality and trends of economic and social development. The purpose of the work is to analyze and systematize the methodology for modeling VAT revenues from imports, justify the use of the econometric method and develop an adequate ARIMA model. It application is possible in the long term as well as smaller periods of time, which is relevant for monitoring and control of tax revenues. The study revealed the main factors influencing the application of the ARIMA model when modeling VAT revenues from imports. The resulting regression model in STATISTICA linked the variables with an accurate approximation.</p>
New methods of robust stability analysis for equilibrium states and optimization of linear dynamic systems are developed. Sufficient stability conditions of the zero state are formulated for a linear control systems with uncertain coefficient matrices and measurable output feedback. In addition, a general quadratic Lyapunov function and ellipsoidal set of stabilizing matrices for the feedback amplification coefficients are given. Application of the results is reduced to solving the systems of linear matrix inequalities.
Introduction. The article examines the trends in the levels of average wages, minimum wages and subsistence minimum, which are extremely important for the analysis of wealth and well-being of the population of Ukraine. The time trends of these indicators are constructed and the regularities of their change during 1996-2020 are established. The Keitz index is calculated and investigated. The dependences of the average wage, the minimum wage and the subsistence level on the gross domestic product are analyzed and established. The values of the values of the mutual correlation function are investigated. Purpose. The purpose of this article is a mathematical and statistical analysis of the dynamics of wages and living wage in Ukraine and the factors influencing them. The task is to study the impact of gross domestic product on the average wage, minimum wage, subsistence level and establish a causal relationship between them using mathematical, statistical and econometric models in order to further predict them and make recommendations on social indicators of living standards. Method. The article uses mathematical and statistical methods and regression-correlation analysis as the main methods of scientific research; time series theory; methods of mathematical modeling. Results. Analyzing the statistical data of indicators of average wages, minimum wages, subsistence level and gross domestic product in Ukraine for 1996-2020, their dynamics is studied. Trend models of wage levels and subsistence level have been built. The general tendency of their growth is noted. Emphasis is placed on the need to use mathematical modeling to study socio-economic indicators of living standards. The Keitz index, which reflects the fight against poverty, is calculated and analyzed. It is noted that during 1996-2009 the subsistence level exceeded the minimum wage. In 2010-2011, the values of the minimum wage slightly exceeded the subsistence level; and in subsequent years, small amounts were observed, until 2017 the minimum wage was not doubled. This positive trend has also been observed in recent years. Econometric models of dependence of average and minimum wage on gross domestic product are presented. The correlation-regression dependence of the subsistence minimum on the gross domestic product is constructed. It is shown that the growth of gross domestic product is accompanied by an increase in social indicators of living standards of the population of Ukraine. The values of the values of the mutual correlation function between the gross domestic product and the levels of wages and subsistence, respectively, are calculated and investigated.
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