The       purpose of the research. The main criterion that determines the living standards of the population in each country is the state of its social protection system. From the point of view of the social protection system, it is possible to provide the population with social benefits, labor pensions and other types of insurance benefits, as well as at the expense of non-state pension funds. The purpose of the study is to study the theoretical and legal aspects of the formation of a system of non-state pension funds and their transformation into the economic system of the country and to substantiate practical proposals in this direction.

The methodology of the research. It consists of studying the system of non-state pension funds in the modern world economy on the basis of statistical materials and making theoretical generalizations in the economic literature written in this direction. At the same time, scientific methods such as statistical analysis, systematic approach, fundamental analysis and so on were used.

The practical importance of research . The study examined the situation of non-state pension funds in the world and their impact on the formation of the social protection system in these sciences using special software. The proposed analysis methodology will allow assessing the role of a country's private pension fund in the social government system.

The results of the research. As a result of the study, the financial opportunities, development features and prospects of non-state pension funds in a number of countries of the world were identified and the comparative situation of non-state pension funds with general macroeconomic indicators was studied.

The originality and scientific novelty of the research. Mathematical and statistical calculations, special software and Excel software were used in the research. The economic indicators of non-state pension funds in a number of developed countries have been studied in relation to macroeconomic indicators.

Keywords: non-state pension funds, objects of security of the operating system, mandatory payments to pension funds, correlation coefficient, investments in private pension funds.