The development of a methodology for the growth of the stock market through a deep transformation of the economic development system and introduction of digital technologies. The article is devoted to the study of the development of stock markets' actual problems that affect the redistribution of capital between sectors of the economy by using tools and mechanisms between the financial and stock markets. The purpose of the study is to improve the regulatory segment of the stock market in order to further develop stock exchanges, integrate them into the global economic system, and attract investment in the economy. To achieve the goal, the following tasks were performed: the development of the London Stock Exchange was analyzed and the profit growth was determined; a comparative capitalization of the main stock instruments was carried out; internal factors of influence on the stock market were determined. The problem of the international stock market in all countries with emerging markets, first of all, lies in the improvement of the institutional environment, which is a prerequisite for the stability of the stock market. To analyze the development of stock markets, natural technical sciences were used to identify objective patterns, and determine the state and motives, using various methods and techniques: logic, generalizations, specific methods of cognition, comparison, and graphics. In the development of the stock market, the economy establishes certain natural actions in the real sector of the economy through a regulatory system of measures, and the needs of investments in the real sector of the economy, methods, and tools are used to achieve the desired results. Statistical, analytical, and dynamic methods were used. The essential foundations of the importance of stock markets and the economy are revealed; we discuss the penetration of knowledge and the conduction of a deep transformation through the introduction of digital technologies in all spheres of the economy, including the transformation of the development of the stock and financial markets nowadays. Results. The assessment of the state of securities markets in developed and developing countries is made on the example of the largest stock exchanges in Brazil and the United Kingdom. The features of the effective functioning of stock markets are revealed. The hypothesis is put forward about the insufficiency of research on the stock market of developed and developing countries and the mechanisms used having an insufficient impact on the development of the economy. From this point of view, an analysis of the dynamics of the current state of the issuers' number and the dynamics of profitability of developed markets is carried out, the comparative capitalization volumes of the stock markets of Great Britain and Brazil are evaluated, and the weaknesses of their functioning are identified. Conclusions. The conducted research shows that countries, where stock markets are successfully functioning and developing, are catalysts for economic development and the accumulation of funds. Each country applies models of stock market development and a strategy for its regulation in accordance with the concept of a functioning market and its maturity.
