In this book we are committed to consistently overcome the above problems within the framework of probabilistic economics according to the following program of actions: developing a mathematical apparatus for calculating ab initio (from the first principles) the temporal fine structure of organized financial markets or exchanges, determining patterns in the functioning of financial markets obtained by comparing theoretical results with experimental data provided by exchanges, and eventually determining the patterns governing these markets, in the strict mathematical language. The patterns thus obtained can be used to derive motion equations that describe the temporal dynamics of market economic systems, in other words, equations that describe the evolution of economies. Thus, the purpose of this study is to create a theory of organized markets that has a sound experimental foundation. Meanwhile, if this venture proves successful, it could be argued that the previously constructed probabilistic economic theory also received a solid experimental foundation.

Using the analogy with the theory of scattering, we can say that probabilistic economics is aimed at solving the direct problem of economics, namely, based on some general principles, to calculate the results of economic activity or economic experiments and to compare them directly with the corresponding experimental data, which will allow to obtain a reliable interpretation of experimental data. At the same time, econometric studies solve the opposite problem – to extract information about the properties of the studied economic system from the experimental data using the help of mathematical methods. In order to avoid misunderstandings, we emphasize that everything that is stated in this monograph, and everything that is asserted in it, unless specifically stated, concerns only the direct problem of economics.

All of the above can be phrased somewhat differently. At the present time, there are two main problems of economic science in the theory of organized markets.

Problem 1 is the almost complete absence of a mathematical body that would allow us to conduct full-fledged theoretical calculations of the details of the exchange markets temporal dynamics at the microscopic level on a small-time scale, for example within 1 hour or one trading session.

Problem 2 is the lack of an experimental basis for economic science in the sense understood in natural sciences: data from systematic theoretical calculations should quantitatively coincide with corresponding experimental data with a satisfactory degree of accuracy.

When solving the above problems, we intend to rely on the physical method of economic research, the main feature of which is the aspiration to find and formulate economic laws in the form of equations, to use to the full extend the mathematical body to perform sufficiently accurate quantitative calculations and constantly rely on experiment in verification of hypotheses, theories and concrete numerical results. This method makes it possible to overcome the shortcomings of the simple empirical method, which currently prevails in economic research, based on a logical analysis of experimental data, as, for example, in the Austrian economic school or in econometric analysis of price dynamics, and to achieve the same level of scientific rigor as in natural sciences, above all physics. Without physical methods of research, i.e., without reliance on experiment, the further development of economic theory is impossible; otherwise, it will long remain in its infancy, in other words, it will remain a kind of protoscience in comparison, say, with natural sciences, above all physics.