The Mathematical Modeling of Exchange Rate Dynamics as a Basis for the State Regulatory Policy

The success of the State regulation of the currency market, which depends on the stabilization of the country’s economy, support for export competitiveness, control of inflation, etc., is determined by the model used as the basis for making managerial decisions. This article proposes two approaches to solving the problem of optimal currency rate regulation. One approach is based on the use of a uniform frequency quality management criterion, while the other relies on the application of an integral quadratic quality management criterion for balancing demand and supply in the currency market. The aim of this work was to build a mathematical model that would allow determining the optimal parameters of the currency market and the conditions under which the deviation of the actual currency rate from the necessary fixed rate would be minimal. Within the proposed mathematical model, it is assumed that all processes considered are continuous in time. This allows for the application of elements of integral and differential calculus for constructing the model. The obtained mathematical model represents a system of differential equations and includes two types of quality criteria that, based on the analysis of possible fluctuations in the exchange rate, allow for the selection of methods for its regulation. However, these criteria have different orientations. Thus, the application of the uniform-frequency criterion is aimed at reducing the volatility of exchange rate deviations from the necessary value under the worst influence of seasonal fluctuations in currency demand. Meanwhile, implementing exchange rate regulation using the integral quadratic quality management criterion allows for the optimization of costs for stabilizing the exchange rate over long time intervals. The results obtained allow for using the proposed mathematical model to substantiate the choice of ways to optimize the regulatory policy of the state in the currency market.