The model of economic self-organization based on the distribution of banking assets

The paper is devoted to the application of methods of the theory of self-organization (synergetics) for the analysis of complex economic and financial systems. Namely, the article proposes a synergistic model to explain the rank distribution of bank assets in Ukraine in the pre-war period. To obtain the ranking formula, we order the banks according to the values of their available assets (at a specific moment within the pre-war period). According to the used scheme, the rank one corresponds to the bank with the largest assets, the rank two corresponds to the bank with the second-largest assets, and so on. Based on the obtained distribution, we determine the functional dependence of the bank assets on the rank. In particular, we propose a phenomenological model which is based on a differential equation. The equation links the change in the value of the bank asset with the change in the bank rank. Based on the model, we solve the equation and get the general form for the approximation function. The function determines the value of the assets depending on the bank rank. It contains a set of parameters that can be determined based on corresponding statistical data. Also in the article, we calculate the rank distribution of the bank assets for the banking system of Ukraine for the pre-war years. Using the described above approach, we propose a functional dependence of the values of bank assets on the bank rank. Based on statistical data, we calculate the phenomenological parameters included in the approximation function. It is shown that for the banking system of Ukraine in the pre-war period, the rank distribution of bank assets in different years is described by the same function (and the type of that function is obtained). We show that within the pre-war period, only the parameters that are included in the function are changed meanwhile the function type is the same. That means that the positions of individual banks in the ranking distribution and their assets could change while the nature of the distribution remains unchanged.