Abstract
The article investigates the problems of the investment management digital transformations at the enterprise, where the instrumental basis based on the system economic theory and integrated IT risk management theory are allocated. The purpose of the study is to develop a recursive and convergence methodology of the investment management of the enterprise digitalization processes. The components of the process of investment digitalization of enterprises are structurally reflected and a deterministic 5-component model of developing a recursive and convergence management methodology based on the digital economy is formed. It is determined that the recursive and conversion methodology is based on the understanding of investment management digital transformations at an enterprise as a complex system, characterized primarily by the diversity and heterogeneity of the constituent elements, numerous internal and external connections, which causes a variety of their interaction, changes in the composition and state of the system. The recursive model provides management of the investment of digitalization in the enterprise as a sequential transition between processes of one level only after all the cycles provided for the current process are implemented. However, such a coherent sequence is possible at the expense of effective information support of each process, which should be implemented on a convergence basis. The precondition for its implementation in the field of digital technologies is civilizational development, consequences of globalization and digitalization.