Дифференциальные уравнения как инструмент исследования экономических систем
Theorems of existence and uniqueness of Cauchy’s problem solution for systems of nonlinear functional and differential equations are proved. During the proof of the theorems the positivity of the Cauchy’s matrix corresponding linear system is used essentially.
Authorities of the state regulation, creditors and investors are interested in getting reliable information about the banking sector activities. The procedure of bank financial soundness and accountability evaluation is carried out by supervision authorities as well as by international and national rating agencies. The analysis of the methodologies of bank accountability evaluation and forecasting in Russia shows the following results. The Bank of Russia makes decisions on banks financial soundness based on financial coefficients of different groups; the calculations are grounded on the official bank statements. Apart from financial indicators, rating agencies evaluate qualitative parameters of the bank activities. The common problem of the bank financial accountability analysis in Russia is the lack of use of the forecasting methods predicting the financial statement of banks and the probability of default. As a result, the problem-free banks corresponding to the demands of the supervision authorities on standards were considered to be problematic during the crisis. The aim of this research is the dynamic analysis of the main indicators of the Russian banks activities at the different stages of the economic cycle in order to identify the indicators of the early bankruptcy prediction and the opportunity to forecast the changes in the bank financial statement.
In this work the demand for the incoming tourism in the Russian Federation is modeling. The panel data for 16 countries - the basic sources of tourist streams - and the period with 2000 for 2009 are used. Modeling is spent separately for each of 10 tourist zones of Russia. In quality a determinant of demand there are considered a total national product in a country of origin, the exchange rate, transport charges, cost of residing, lag of the demand variable and the fictitious variables reflecting influence of shocks in quality a determinants of demand. The received estimations of dynamic models of demand correspond to expectations, are statistically significant and can be useful in practice of planning of development of entrance tourism in various municipal formations and regions of Russia.