Ekonomichna kibernetyka [Economic cybernetics]

4-11

Authors: Zabolotskyy T.N., Vitlinskyy V.V.

Purpose and subject of research This study investigates the problem of rational choice of portfolio structure using the expected utility based on Value-at-Risk. Research methodology The study used formal mathematical methods, the method of economic and mathematical modeling, methods of portfolio construction, analytical methods of research. Value results We discuss the correctness of sample estimator of rational structure weights. Specifically, we define densities of the sample estimators for main portfolio characteristics and elaborate how the densities depend on investors' risk aversion coefficient. Our empirical tests allow us to give some recommendations about the rational choice of the coefficient based on the data from PFTS Ukrainian stock exchange market. It is shown that the high values (larger than 4) of this coefficient should be avoided as well as the low values (in the neighborhood of one). Conclusions The paper examines properties of portfolio characteristics with maximum expected utility based on Value-at-Risk. The use of this risk measure in portfolio theory is fully consistent with recommendations of the main banking documents. From the theoretical point of view application of expected utility function for portfolio constructing is a generalization of the portfolio constructing problem with minimum risk and given level of portfolio return. Key words: portfolio construction, Value-at-Risk, rational structure weights, portfolio characteristics.

19-26

Authors: Vitlinskyi V.V., Koliada Y.V., Perten S.I.

Purpose and subject of research The aim of the article is to highlight the mathematical formalization basic principles of the approximate inflation kinetic models solutions, the exact solutions of which are obtained only by numerical integration. Research methodology The basis in achieving this goal is the detailed analysis of the numerical solutions integral curves, which allowed to identify and formulate changes in the behavior of numerical solution, and caused the changes in the model parameters values. Value results An approach described in the article expands the range of possibilities in the modeling of inflation processes, namely: the prediction of their quantitative level for particular conditions; the creation of alternative development scenarios; the definition of anti-inflation measures necessary to achieve the optimal rate of inflation for the economy. Approximate solutions in the analytical form based on exponential functions are offered. The estimation error of the abovementioned solutions is implemented. The formulas of the peak significance computation of the inflationary surge, which took place in the result of money supply increase, are obtained. Conclusions The approximate analytical solutions of the model are made, that facilitates the transition to the next quality level of the inflation processes development within the inflation kinetic model. Key words: kinetic models, modeling of inflation processes, money supply increase, approximate analytical solution.

31-38

Authors: Isaienko A.A., Glushchevsky V.V., Isaienko A.N.

Purpose and subject of research The actual problem of modeling of the multivariate nonstationary time series of economic dynamics is being researched for the purpose of analysis, forecasting and decision-making in financial markets. Research methodology The proposed approach to the modeling of time series is based on the methodology of multivariate analysis and continuity equation, which relates the probability density function of the state variables of the system with their speeds. Value results Equation of motion of a point in a multidimensional phase space of state variables derived under the assumption that the evolution of the economic system based on the interaction of two factors - the growth and dissipation. It is assumed that the growth rate has a deterministic function, which means that there is a causal link between variables, and the diffusion component of the velocity is proportional to the gradient of the state probabilities in a local point of phase space. In this case the state of the system is determined by multivariate Fokker-Planck equation. On the basis of two-dimensional Fokker-Planck equations is constructed model of the real economic process - trading on the stock exchange. The structure of the model equations of nonlinear responsible paradigm of financial markets and agreed with the results of empirical research. We derive differential equations for the evolution of one-dimensional distributions of prices, trading volume, and spread their moments that are needed to complete the system for the unknown probability density functions. Conclusions The evolution equations are based on sample data and agreed with the two-dimensional Fokker- Planck equation. Modeling the dynamics and forecasting of trades carried out by numerical integration of the equations of evolution in a sliding window of the sample. The proposed approach to modeling allows the best use of the information contained in the multivariate time series and to obtain high prediction accuracy. Verification of the model performed on the rows indices trading on the Ukrainian stock market. Key words: multivariate time series, Fokker-Planck equation, forecasting, stock exchange.

43-50

Authors: Babenko V.A.

Purpose and subject of research The main approaches in the identification of parameters of economic and mathematical models are considered, the problem of a posteriori identification of the dynamical model parameters of innovative process management of reprocessing agricultural enterprises is researched. Research methodology Solutions for a posteriori identification of parameters of the dynamic model of innovative process management of reprocessing agricultural enterprises propose an algorithm that reduces to the implementation of solutions of systems of linear algebraic equations, the formation of the linear regression equation and use the method of least squares. Value results An algorithm for solving the problem of a posteriori identification of parameters of the dynamic model of innovative process management of reprocessing agricultural enterprises proposed algorithm makes it possible to develop efficient numerical procedures to implement a computer simulation of the dynamics of the system of innovative process management of agricultural enterprises. Conclusions Results presented in this paper can be used for economic-mathematical modeling and solving optimization processes of forecasting and data management in a lack of information and the availability of risk, as well as for the development of appropriate software and hardware systems to support effective management decisions in practice. Key words: posteriori identification, innovation process in agriculture, economic and mathematical modeling, discrete dynamical system, the risks of agricultural production.

56-63

Authors: Serduk V.N., Zorina M.S.

Purpose and subject of research This article describes the features of strategy management of an industrial enterprise financial resources, the conditions for increasing its efficiency and proposed economic- mathematical model of the mechanism of forecasting indicators strategic financial management of an industrial enterprise, which improves the efficiency of operation of the business through improved management of financial resources , to improve the accuracy and timeliness of management decisions based on a scenario assess the economic impact of the use of different measures for financial management of an industrial enterprise. Research methodology The theoretical framework is based on the methods of system analysis to the business management of the financial sector, innovative models of financial management, modern methods of economic cybernetics. Value results The main of this model are five scenarios for allocating financial resources of the industrial enterprises in the respective activity. Conclusions According to the results of simulation experiments, we can conclude that the application of the economic-mathematical model to minimize the cost of financial resources and the value of their involvement. Addressing financial management is the foundation of efficiency, competitiveness and financial sustainability of the Ukrainian industrial enterprises. Key words: industrial enterprises, financial resources, strategies indicators, mechanism of prediction.