Mathematical Models for Implementation of the Concept of Hard budget Restrictions in the budgetary system

 The subject of the study is the processes of budget decentralization in the management of public finances, as well
as mathematical methods and models for implementing the concept of hard budget restrictions in order to create conditions for the self-development of administrative-territorial units.

The aim of the study is to develop adaptive economic and mathematical models for implementing the strategy of hard budget constraints implemented in the process  of inter-budget regulation.

The relevance of the study is due to the fact that currently the subject of acute discussion in the scientific community is the self-development of administrative-territorial entities and increasing their financial independence. In this regard, the focus of economic research is focused on the problems of budgetary decentralization as an engine of economic development, as well as the related topics of the use of mathematical tools for modeling decision support in this area. The created models are subject to the requirements of learnability, adaptability to changing conditions of environmental influences, and the ability to operate not only with quantitative, but also with qualitatively defined characteristics. The problem of mathematical modeling is solved by applying an interdisciplinary synthesis of the theories of stochastic automata operating in random environments and fuzzy logic.

The proposed synthesis of theoretical and methodological devices is the novelty of the research.

As a result, an economic and mathematical model of a fuzzy automaton is constructed for determining and quantifying the values of the norms for the distribution of tax revenues between budgets of different levels of the budget system. A fuzzy automaton interacts with a simulation model that reproduces budget flows and quantifies the decisions made by the automaton model.

The practical significance of the research results lies in the program implementation of the developed models and their inclusion in the public finance management circuit. In the future, it is planned to create a mathematical model of the collective behavior of fuzzy automata models, the interaction of which solves the problem of coordinating the interests of budgets of different levels of the hierarchy in the distribution of tax revenues. 

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