Вероятностная теория фондовых бирж

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.