The relevance of the study is due to the development of the digital economy in the Russian Federation. Forecasting, strategic planning in this aspect is a promising direction of socio-economic development of the state, as well as its constituent parts – regions, municipalities, enterprises (firms) – the latter being on the lower level of the economy forming its foundation. This area of research provides a methodological basis for the development and implementation of management decisions focused on priority areas of economic development of the state. The purpose of the study is to analyze and develop theoretical and methodological provisions of strategic and innovative development of the multi-level economic system of the state in the digital economy. Other objectives include the research and development of mathematical models of the lower level of the state economy of large corporations (clusters). To achieve these goals, the first part of the work examines the structure of a multi-level hierarchical system of the state economy aimed at solving the problems of strategic planning and management at individual levels of the state within the digital economy. In the second part, based on the analysis and theoretical studies of previously proposed mathematical models of enterprise development, we developed a mathematical model of a corporation (cluster). The cluster model takes into account both extensive and intensive factors of production development. The input data of the cluster model is, first, statistical information and, second, technological information of pre-production. It is shown that taken together statistical, technological information, as well as the relationship with consumers of products and with the financial (banking) sphere is characterized as “digital economy”. The direction of further research is related to the practical implementation of mathematical models and their use in the practice of forecasting the development of an industrial corporation (cluster).