Вероятностная теория фондовых бирж. Анатолий Васильевич Кондратенко
reliable forecasts of economic development.
This monograph demonstrates the theory’s validity, and precisely the way in which it is better than other theories. Its effectiveness is shown when applied to important, organized markets such as stock exchanges. Based on the obtained results, a method is proposed for forecasting economic dynamics. Below, I will explain why stock exchanges were chosen as the objects of research.
It is well known that the division of labor by the various producers of goods improved the well-being of humankind during the early stages of civilization. This led to the subsequent formation and development of capitalism across the world. Initially, this process was dominated by ordinary markets, which facilitated and thereby accelerated the process of goods and services exchange between people. Eventually, this evolved to occur between organized markets, the more complex of which we have today such as the commodity, financial, and currency markets, amongst others. Together, their existence forms the exchange economy.
Currently, this exchange economy has, and effectively uses, all the most modern means of e-commerce, including artificial intelligence and algorithmic computer trading. Fueled by the widespread use of the Internet, the exchange economy is lightning fast, virtual and truly global. It is the high speed of information exchange and number of transactions that distinguishes the new virtual exchange economy from the traditional real economy. However, this feature of exchange trading can generate additional risks, both for the exchange economy and for the real economy. To date, these risks are only superficially understood in the economic academic community.
In today’s global economic world, the role of exchanges has become so significant that it is no exaggeration to say that the entire global economy is increasingly evolving towards an exchange economy. It would be more appropriately referred to as the transformation of the global economy into a financial economy, but in this monograph we will focus only on the role of exchanges in the economy. Therefore, we will use the term «exchange economy».
In today’s economy, the main purpose of exchanges is to determine prices for all tradable assets, including various types of money (currencies). Exchanges also facilitate trading and finance global economic activity. However, it is important to note that the state of affairs of all exchanges are good indicators of the entire global economic situation. The paradox of this status in the global exchange world is that there is clearly no adequate status in the world of theoretical finance. An adequate theory of organized financial markets still does not exist, which means there is no adequate theory representing the global real economy. This situation generates certain risks of the emergence and uncontrolled development of negative trends in the financial markets. This can lead to large-scale financial and, in turn, global economic crises, which we regularly observe in real life.
The generator of almost all economic crises in modern history are financial crises, the trigger of which are exchange crashes. Currently, the situation is exacerbated and the risks are increasing. This is because the bulk of transactions are now made by computers. Working strictly according to algorithms aimed mainly at achieving quick results, they guarantee the absence of even minimal losses. They act almost synchronously, which can cause a chain reaction of collapse on the exchanges in isolation from the real state of affairs in the economy, and from the real value of assets. Meanwhile, regulators have no meaningful or reliable tools to monitor or manage any particularly volatile situations in the financial markets.
This is particularly valid in organized markets or exchanges where the prices of all global goods and assets are largely measured. All these management processes are currently reliant on tools using the analysis of accumulated historical experience and the use of empirical parametric models [Intriligator, 1971]. Therefore, overcoming the obvious stagnation in the development of theoretical finance is a long-overdue global task. The main challenge now is to overcome the near complete absence of a mathematical apparatus with which to describe the functioning of the exchange as an asset-pricing mechanism. Financial econometrics can do this qualitatively, but also required is the ability to calculate the temporal fine structure of the price and trade volume dynamics within short time intervals, such as during a single trading session.
Using a parallel with the physics theory of scattering, we can look at this differently. Econometrics focuses on solving the so-called «inverse problem», namely, the problem of extracting information from experimental data about the system under study. Conversely, we aim to solve a direct problem: the creation of a near-universal method of calculation from the first principles (ab initio) of the temporal exchange microstructures. These, with a characteristic time size of several temporal seconds, can be directly compared with the corresponding experimental fine structures of trading dynamics. This method could serve as a powerful tool for building a quantitative theory of exchanges.
We hope that in future, the probabilistic theory of exchanges developed in this study can serve as a basis for building a more general probabilistic financial theory. In doing so, a deeper understanding will be gained of how our global world of finance works.
It is obvious that organized markets are complex, multi-agent, non-equilibrium probabilistic systems, the description of which requires the application of adequate mathematical methods and apparatuses. The only suitable source of such methods and apparatuses is physics, where the experience of theoretical work with multiparticle systems with similar, formal structures has long been accumulated. In addition, quite a lot of experience has already been gathered in the application of the physical method in economics, namely, the use of formal methods and approaches of theoretical physics in solving economic problems.
In particular, probabilistic economic theory was developed [Kondratenko, 2005, 2015], a new theory of market economy. Initially, this theory was modeled on quantum mechanics with the derivation of economic equations of motion. Unfortunately, we are not yet able to accurately solve these equations for multi-agent markets. Because of this, a simpler version of the theory was later developed. It uses only the probabilistic method without solving equations of motion, namely, probability economics. It is used in this work as a basic theory for constructing probabilistic theory of exchanges. Although it contains no equations of motion, there is a mathematical apparatus that has proven very adequate and fruitful for describing exchange processes and structures.
To clarify, probability economics contains neither physics nor mechanics and, in particular, no quantum mechanics. This is an economic theory used to describe economic processes taking place on exchanges. This theory uses a mathematical apparatus which was created hundreds of years ago, and was previously used successfully to solve similar problems in physics. Probability economics has been developed in the spirit of both classical economic theory, and the physical method in economics. This variant has followed a figuratively similar evolutionary trajectory to the theories of Adam Smith to Karl Menger and onwards to Ludwig von Mises.
The works of these three authors have fostered my understanding of the essence and tasks of real economic science, as well as the desire to develop their ideas and concepts using the modern scientific probabilistic method of research. My primary task has been the creation of a mathematical apparatus adequate to the physical method and its use for the calculation of real economic systems. A similar process occurred during the creation and rapid rise of physical science, due to the creation of a powerful mathematical apparatus. It began with the discovery of the equations of motion and differential calculus.
The probabilistic method has long been applied at the empirical level in economic research by using the basic formulas of probability theory. The use of the probabilistic method in economics used an analogy with quantum mechanics of physical multiparticle systems [Kondratenko, 2005, 2015], and broadly pushed forward the framework of ideas and conceptions about the modern economic world. It gave rise to a new, probabilistic style of scientific economic thinking and created a new, dynamic probabilistic picture of the modern economic world. This veered away from the traditional static ideas of the economic mainstream, including neoclassical economic theory. This monograph solves the problem of this approach’s practical application to specific economic systems, or exchanges. There is enough input data in the form of supply and demand quotations for quantitative study, as well as enough relevant, experimental data in the form of market prices and trade volumes to verify the theory.
Probability economics is built in terms of probability distributions. These are usually accepted in various scientific