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Finance and Credit
 

Solving systems of homogeneous linear algebraic equations in pricing problems of an alternative financial model

Vol. 30, Iss. 1, JANUARY 2024

Received: 30 October 2023

Received in revised form: 23 November 2023

Accepted: 7 December 2023

Available online: 30 January 2024

Subject Heading: Financial system

JEL Classification: O10, O11, O21, P41, P42

Pages: 124–144

https://doi.org/10.24891/fc.30.1.124

Sergei A. KUZNETSOV Tula State University (TulSU), Tula, Russian Federation
kca.kuznetsov@yandex.ru

ORCID id: not available

Nataliya E. GUCHEK Tula State University (TulSU), Tula, Russian Federation
guchekne@mail.ru

ORCID id: not available

Aleksandr V. OGNYANOVICH Tula State University (TulSU), Tula, Russian Federation
oavsoft@mail.ru

ORCID id: not available

Sergei S. KUZNETSOV Tula State University (TulSU), Tula, Russian Federation
su-30mki.ru@yandex.ru

ORCID id: not available

Elizaveta D. BLAGOVESHCHENSKAYA Higher School of State Audit of Lomonosov Moscow State University, Moscow, Russian Federation
office@audit.msu.ru

ORCID id: not available

Subject. This article focuses on the problems of solving systems of homogeneous linear algebraic equations in the pricing problems of an alternative financial model.
Objectives. The article aims to develop a non-trivial approach to solving the problem of pricing from the scratch in the construction of a national alternative financial model, which boils down to solving large homogeneous systems of linear algebraic equations, complicated by the fuzzy setting of initial parameters (initial data) within the framework of creating a State model of a socially oriented economy, guaranteed to ensure economic, military and other types of integrated security of the Russian Federation.
Methods. For the study, we used tensorial notations involving the use of elements of linear algebra, including operations with matrices and vectors, the apparatus of the fuzzy set theory (interval arithmetic), as well as methods and principles of scientific research and complex logical analysis and modeling of pricing and technological processes.
Results. The article shows that an effective non-zero (different from zero, i.e. classical, trivial) solution of systems of homogeneous algebraic equations in pricing problems of an alternative financial model from the scratch is possible if the initial parameters are specified by fuzzy sets, which significantly simplifies the procedure of the computational process and the volume of arithmetic operations.
Conclusions. The results obtained can be used in structures involved in the creation and testing of financial and economic models both at the federal and the Russian Federation constituent entity levels, as well as in governmental and non-governmental organizations dealing with the issues of pricing, planning and logistics support for business entities not only in the Russian Federation, but also in other countries experiencing problems in the field of financing.

Keywords: financial model, pricing, system of homogeneous linear algebraic equations

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