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.
First, we will very briefly express a subjective opinion about the state of modern economic science, so that the reader could understand the logic of the research undertaken in this work and its main objectives, and, ultimately, the value of the results obtained. We will formulate our opinion in the form of two statements.
Statement one. In our view, all old and new, widely known economic theories, including neoclassical economics, Marxist and Keynesian theories, the Austrian economic school and other currents of economic thought are, in fact, either heuristic or, at best, empirical theories with neither clear unambiguous experimental results, nor rigorous mathematical theories that allow ab initio calculations on the dynamics of specific real market systems whose results coincide with the corresponding experimental results of these markets work with a reliable level of accuracy. Moreover, proponents of even the most logically advanced empirical economic theory, namely the Austrian economic school, argue [Von Mises, 2005; De Soto, 2009] that neither experimentation nor even the use of the mathematical apparatus to describe economic phenomena and market processes is possible in principle. On this basis they categorically denounce all attempts to use the achievements of physics and mathematics for development of the quantitative economic theory. In our opinion, the current situation in economics is not absolute; it only repeats the similar situation that existed in physics 300–600 years ago before the works of Nicholas Copernicus, Isaac Newton, Galileo Galilei and other physicists and mathematicians of the new era in physics. What is the main reason for economics to lag behind physics for so long in this respect? John von Neumann and Oskar Morgenstern provide an excellent answer to this question in the quote from their book given in the epigraph. The reason was hidden in an objective factor, namely in the very absence of the possibility to rely on experiment in economics, at least in the form of systematic long-term observations of the cyclic motion of the planets of the solar system, as was done in physics. At present such an opportunity is provided to us by electronic exchanges with their digital platforms and big data that can be used, in general, for the verification and development of economic theories.
Returning to the beginning of the discussion, let us note that the probabilistic economics we developed was also empirical or heuristic in content, based on our twenty-five years of entrepreneurial experience in the investment business. So, in this respect it is no better than any other economic theory; thus, it is virtually unknown in the scientific economic community. But there is an important nuance. Unlike all other theories, probabilistic economics has a developed mathematical body suitable for calculation of any market economic systems. The results of these calculations can be compared with known experimental data, for example for exchanges. In this regard, in this study we have set a goal to find experimental evidence that the very foundations of probabilistic economics are valid, in other words, to verify the initial premises and assumptions of the theory by means of experiments. Moreover, this should be done the way it is done in physics, namely by continuously comparing the results of ab initio calculations of the dynamics of exchange systems and the results of experiment, as well as by subsequently confirming or rejecting the assumptions made. Only this approach, or method of investigation, which we call the physical method in economic science and which is universally recognized in the natural sciences, will make it possible to develop an adequate economic theory capable of giving a sufficiently accurate quantitative description of how real markets of any complexity work, as well as of making sufficiently reliable forecasts of markets and economies development, at least in the short term. In other words, we aim thereby to establish sufficiently accurate experimental justifications for economic science.
Statement two. Let’s recall the great importance of the long-term observations of the solar system planets behavior [Smith, 2016] in the development of modern physics and what John von Neumann said (see above). Richard Feynman was of the same opinion: "Astronomy is older than physics. In fact, physics emerged from it when astronomy noticed the striking simplicity of stars and planets motion; the explanation of this simplicity was the beginning of physics.” Figuratively speaking, the solar system played the role of the first experimental physical laboratory in the history of science. Of course, it was impossible to perform experiments on it in the modern sense of the word, but it was possible to observe the motion of the planets without interference for a long time, and based on these observations the scientists could try to find the rules governing this motion, and even calculate the trajectories of the planets, which was actually done [Feynman et al., 1978; Smith, 2016]. Fortunately, this movement was frequent enough, almost exactly the same, that it allowed us to observe the same phenomena for quite a long time. And the strict periodicity in the planets motion clearly indicated the existence of strict rules governing this motion. It was just a matter of discovering them.
What about economics? Fortunately, we have at our disposal a wonderful experimental economic laboratory that has the potential to brilliantly play the same role in economics that the solar system has played in physics. These are, of course, the exchanges that determine the market prices of goods, services and, especially important in today's economic world, financial assets of various kinds. Physically speaking, exchanges measure prices at each moment of trading, which are unconditionally accepted by the economic community as market prices, i.e., as valid and fair. By measuring market prices and making them universally available, exchanges play an enormous role in modern economic life, providing everyone with a basis for making crucial economic decisions. Despite the important role of exchanges in the real economy, the importance of exchanges in economic theory is far from significant for the reason that a sufficiently developed theory of the exchange capable of adequately describing the dynamics of exchange prices in real time is not available in literature, as far as we know (see, for example, reviews in [Ippoliti and Cheng, 2017]). It is our purpose in this paper to develop such a dynamic economic theory, and fulfillment of such purpose, among other things, will help to confirm (or refute) the foundations of probabilistic economic theory, which is of particular interest to us. Looking ahead, we note that here, we also found the same "striking simplicity of movement" of market agents, despite the fact that the exchange, without any doubt, is a complex dynamic nonequilibrium probabilistic system.
We have selected several different