A REVIEW OF THE METHODS OF ECONOMIC AND MATHEMATICAL MODELING BASED ON THE PRINCIPLES OF ECONOPHYSICS. PART 1

Abstract

A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics is given. The first part gives the concept of a financial bubble and methods for their search. The review covers the period 2010-2019. A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of information systems and mathematical methods in Economics is given. The first part gives the concept of a financial bubble and methods for finding them. At the beginning of the article, the development of econophysics is given. Therefore, using the research of physicists as a model, econophysics should begin its research not from the upper floors of an economic building (in the form of financial markets, distribution of returns on financial assets, etc.), but from its fundamental foundations or, in the words of physicists, from elementary economic objects and forms of their movement (labor, its productivity, etc.). Only in this way can econophysics find its subject of study and become a "new form of economic theory". Further, the main prerequisites of financial bubble models in the market are considered: the principle of the absence of arbitrage opportunities, the existence of rational agents, a risk-driven model, and a price-driven model. A well-known nonlinear LPPL model (log periodic power law model) was proposed. In the works of V. O. Arbuzov, it was proposed to use procedures for selecting models. Namely, basic selection, "stationarity" filtering, and spectral analysis were introduced. The results of the model were presented in the works of D. Sornette and his students. The second part gives the concept of percolation and its application in Economics. We will consider a mathematical model proposed by J. P. Bouchaud, D. Stauffer, and D. Sornette that recreates the behavior of an agent in the market and their interaction, geometrically describing a phase transition of the second kind. In this model, the price of an asset in a single time interval changes in proportion to the difference between supply and demand in this market. The key situation to study is the moment of formation of an infinite cluster on the percolation grid, since this means the collapse of the market, when the overwhelming part of agents for this market has a similar opinion about their actions to buy or sell an asset. The main characteristics of the process are the threshold probability of market collapse, as well as the empirical distribution function of price changes in this market.