Subject. The article underpins of the need to build a national financial system which will fully guarantee addressing socio-economic problems. Objectives. The purpose is to create fundamental institutions for development of national concepts of economic and financial models, pricing methodologies, approaches designed to build a State model of a socially oriented economy that guarantees the functioning of all branches of financial and economic activity, and military, economic, and other types of national integrated security. Methods. The paper uses tensor notation involving the use of elements of linear algebra, including operations with matrices and vectors, interval mathematics, and a set of methods and principles of scientific research and complex logical analysis and modeling of product and financial flows. Results. We show the possibility of obtaining the country's resources for free when creating a shortage of means of payment under implementation of the basic principle of a market economy, i.e. free pricing. The paper offers financial and economic models of the main participants of financial and economic activity: legal entities, individuals, and State-owned enterprises and organizations. On their basis, we demonstrate closed cycles of money circulation, which formed the basis for building a national financial model. We propose to construct financial models using interval analysis, which correlates with the specifics of measured parameters in the financial and economic sphere. Conclusions. The suggested approach is confirmed by the results of trial calculations. It has practical significance not only for the Russian economy, but can also be used in other countries.
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