The article develops economic and mathematical models as a tool for conducting factor financial analysis of the prospects for the development of an industrial enterprise. The functioning of the developed economic and mathematical models is based on the DuPont model, which allows analyzing the dynamics of the company’s profitability in the course of two-factor and three-factor financial analysis. The proposed model tools are based on the convergence of deterministic financial analysis methods embedded in the DuPont model and simulation methods that allow analysis under the influence of random factors. The constructed economic and mathematical models for forecasting profitability use the company’s retrospective data on its financial condition: the amount of profit, revenue, assets, and equity. The constructed simulation models are implemented in the OMEGA software product and included in the computer technology for predicting the profitability of an industrial enterprise. The architecture of the proposed tools is presented, and the results of simulation experiments performed on models are demonstrated.

This article is devoted to the creation of intelligent modelling tools for decision support in the evaluation of intellectual projects submitted for financing, as based on qualitatively defined characteristics. The economic and mathematical models that form the basis of the toolkit are constructed using the mathematical apparatus of fuzzy logic, which allows for the description of poorly structured knowledge of specialists, as well as their application in solving questions about the extent of the impact of the proposed projects on the environment. The authors classify investment projects according to the degree of impact on the environment, the environmental criteria required by the investor for the evaluation of investment projects, and the formal formulation of the problem of evaluation of investment projects when taking into account the environmental factor. The toolkit was created based on the concept of intellectualization, where economic and mathematical models for the evaluation of investment projects are programmatically implemented via the tools and functions available in the MATLAB package.

The article is devoted to the improvement of decision-making processes in the management of inter-budgetary relations between the regions and depressed mining municipalities. The tools of decision-making support in the form of economic and mathematical models included in the control circuit are proposed. Economic and mathematical tools are based on the application of the mathematical apparatus of the theory of stochastic automata in random environments. The constructed mathematical abstraction “stochastic automaton” describes the behavior of the decision-making subject in determining the norms of shared distribution of tax revenues between budgets on the vertical line of power. A stochastic automaton possesses the property of learningability of expedient behavior. The decisions made by the automaton regarding the values of the tax revenue distribution norms are quantified through interaction with the simulation model. The simulation model forms a random environment in which the stochastic automaton is immersed, and reacts to the administrative decisions made by the automaton through its encouragement and punishment. The article proposes the construction of a stochastic automaton, described by its transition function. The transition function of an automaton from state to state is formally represented by matrices. The authors derive analytical expressions for the final probabilities of the machine in each of its states. The efficiency of the economic and mathematical tools is demonstrated through the presentation of the results of the conducted experimental studies in the selection of options for decisions regarding the share of the distribution of tax revenues.