Modeling the Control Effects of the Banking System on the Functioning of the Economy. II. Selection and Special Features
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MODELING THE CONTROL EFFECTS OF THE BANKING SYSTEM ON THE FUNCTIONING OF THE ECONOMY. II. SELECTION AND SPECIAL FEATURES OF APPLICATION OF OPTIMIZATION ALGORITHMS*
V. V. Khilenko
UDC 519-7/339.9
Abstract. The mathematical formalism of accounting of the effects of splashing out, foaming, and reverse momentum in the formation of complete mathematical models of the dynamics of the financial-economic systems is considered. An algorithm is determined for applying the well-known two-stage optimization schemes for calculating optimal control actions. Keywords: financial-economic system, mathematical modeling, calculation and forecasting of dynamics, optimization of control, calculation of control actions, effects of splashing out, foaming out, and reverse impulse. This paper continues the study [1]. The characteristic properties of the full mathematical model (SM model) of the financial-economic system (FES) presented in [2] leave the study of dynamics of this model class, the choice of mathematical apparatus and transformation algorithms, which ensure their effective analysis and calculation in the feasible time interval relevant. At the same time, aggregation of the FES SM model is due to tracking the variations and analyzing the current values of a limited number of particular indicators (markers of the FES state), which play a decisive role in the transition of the system trajectory to the intervals that correspond to stagnation or the crisis state of the economy [2]. As it is known [3], the splashing out effect, as well as the foaming out and the reverse impulse effects [1, 2] have a significant impact on the overall dynamics of the global FES, which is reflected in the change of the state marker values. These effects belong to the factors whose mathematical formalization is necessary to ensure the adequacy of the used mathematical model of the FES dynamics and, consequently, the correct calculation of control actions. A comparison of the calculated (predicted) values of the FES state markers in real time with certain boundary values, which were established and specified in the corresponding Pareto set, as well as timely detection of the foaming out effect, will allow us to predict the impending crisis and to assess the time interval Dt before the significant manifestation of undesirable changes in the system dynamics. The numerical boundary values of the Pareto set data (as well as questions of forming an optimal storage structure for the aforementioned boundary values) for the problems considered below will be regarded as given. Solutions to their determination problems can be obtained either by expert assessments of specialists, or by iterative mathematical modeling in order to find the maximum correspondence between the macroeconomic processes and their mathematical models. The subject of this article is the definition of the mathematical formalism used to calculate the FES SM models, taking into consideration their features [2], and the influence of the splashing out, foaming out, and reverse impulse effects.
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