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Nowadays, studying the categories of "economic sustainability", "economic sustainability management" and the peculiarities of these concepts is especially relevant. Their use would provide an opportunity to ensure the sustainable and most effective functioning of the subject of economic relations in the current period of time, as well as to create a high potential for its development and ensuring the conditions for investing capital in the Ukrainian economy. All this determined the purpose of this study, which consists in the analysis of the theory and essence of the economic sustainability concept, the interpretation of the concept of "economic sustainability of the system" and the concept of "management of economic sustainability of the system", distinguishing factors affecting the sustainability of the Ukrainian economic system, determining the relationship of economic sustainability with economic security, investing as well as forecasting the level of the Ukrainian economy sustainability based on the innovative modeling methods. The object of the research is to develop the theory of the "economic sustainability" concept and to determine the level of economic sustainability of the economy aimed at raising the investment climate in Ukraine. To ensure the development, security and investment attractiveness of the Ukrainian economy, an organizational structure of the management model for the sustainability of the Ukrainian economic system was developed using the developed economic and mathematical model.

The influence of budgetary risks on the formation of revenues of budgets of territorial communities is investigated and a methodical approach to estimating the structure of revenues of budgets of territorial communities in the conditions of financial decentralization is developed. It is noted that today the introduction of the latest methods for optimizing the revenues of the budgets of territorial communities with permanent control over the level of budgetary risks becomes especially important. Mathematical forecasting of the probability of budget risks and its empirical measurement requires special attention. The main approaches of domestic and foreign scientists to forecasting the probability of budget risks with the help of economic and mathematical tools are considered. Its practical use, on the one hand, will ensure their permanent control, and on the other - will allow optimization of the revenues of the budgets of territorial communities. It is established that the existing methods are difficult to implement in domestic practice due to their significant mathematical calculation. Calculations were made using the postulates of portfolio theory, in particular the portfolio approach of J. Hicks, which allowed to form a rational structure of revenues of budgets of territorial communities in terms of general and special funds, as well as to identify ways to minimize budgetary risks to ensure optimal revenue structure without interbudgetary transfers in conditions of permanent crisis phenomena. This will allow local governments of territorial communities to increase the performance of their budgets. The latest tools of financial decision-making using J. Hicks' portfolio approach to the formation of the optimal structure of budget revenues of territorial communities without intergovernmental transfers, taking into account the level of budgetary risk, were obtained by applying the tools of economic and mathematical modeling. It is concluded that the latest tools for the formation of the optimal structure of budget revenues of territorial communities with permanent forecasting of the maximum possible level of their growth under the control of budget risks allow the development of ways to minimize, forming many scenarios for the optimal structure of future budget revenues and budget risk. It is established that the proposed toolkit allows to generate alternative financial solutions for local governments and assess the results and consequences of their possible adoption in determining strategic guidelines for the development of local community finances. It is proposed to further use the developed scientific and methodological approach to optimize the revenue structure of budgets of territorial communities in the context of various budgetary risks, which, of course, will allow local governments to make effective financial decisions in developing programs of socio-economic development of territorial communities.

The purpose of the paper is to study the current state and trends in the development of the basic indicators of the EU gas sector, to generalize the theoretical and methodological approaches to calculating the gas diversification factor, assess and analyze its level in the EU countries in 2001-2015, and study the experience of European countries in addressing the diversification problems. Methodology. The methodological basis of the study was the works of domestic and foreign scientists devoted to the issues of gas supply diversification. The study is based on the analysis of the gas sector indicators and used analysis, synthesis, combination grouping and statistical-economic methods. Results of the of the study showed that in the EU countries in recent years there has been a noticeable tendency to reduce natural gas reserves, reduce the level of its production and increase consumption, which leads to an increase in import dependence. The largest consumers of natural gas in the EU are the United Kingdom, Germany, Italy, the Netherlands and France. The main external importers of pipeline gas to the EU countries are the Russian Federation, Algeria and Norway, and liquefied gas-Qatar, Algeria and Nigeria. It is established that at the end of 2015, the most diversified gas supply is to countries such as France, Belgium and Italy; a low level of gas supply diversification is observed in Hungary, Poland and Greece. Practical implications. The analysis of basic indicators which characterize the state and development of trends of the European gas market in 2000-2015 is carried out. The assessment and analysis of the level of diversification of natural gas supplies in the EU countries in 2001-2015 have been analyzed. Value/originality. It was proposed an original approach to calculate the gas diversification factor, which takes into account both the number of sources and the structure of the volumes of supplies from different sources.