Y.N. Perevyshin
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FREQUENTLY USED SYMBOLS
Г– agent width
MOEX – Moscow Exchange
BRENT – Brent oil futures
C – normalization factors
D – demand
D(t, p, q) – probabilistic market demand function
D0(t) – total market demand function
ICE – Intercontinental Exchange Futures Europe
F(t, p, q) – probabilistic market deal function
M(t)– number of supply quotations
N(t) – number of demand quotations
MTV(t) – probabilistic market trade volume
P – price
p – independent price variable
pM – probabilistic market price
q – independent quantity variable
qM– probabilistic market quantity
Q – quantity
PQ – price and quantity
S – supply
SBER – Sberbank shares
S D – supply and demand
S(t, p, q) – probabilistic market supply function
S0(t) – total market supply function
t – independent time variable
TV(t) – trade volume
T – time
USD/RUB – USD/RUB futures at MOEX: U.S. dollars are traded for Russian rubles (₽).
INTRODUCTION
"The impartial observer can have no doubt about the reason our generation pays general and enthusiastic tribute to progress in the field of the natural Sciences, while economic Science receives little attention and its value is seriously questioned by the very men in society to whom it should provide a guide for practical action. Never was there an age that placed economic interests higher than does our own. Never was the need of a scientific foundation for economic affairs felt more generally or more acutely. And never was the ability of practical men to utilize the achievements of Science, in all fields of human activity, greater than in our day. If practical men, therefore, rely wholly on their own experience, and disregard our Science in its present state of development, it cannot be due to a lack of serious interest or ability on their part. Nor can their disregard be the result of a haughty rejection of the deeper insight a true Science would give into the circumstances and relationships determining the outcome of their activity. The cause of such remarkable indifference must not be sought elsewhere than in the present state of our Science itself, in the sterility of all past endeavors to find its empirical foundations. The reason for this conspicuous indifference is none other than the present state of science itself, the fruitlessness of hitherto attempts to comprehend its empirical foundations".
Carl Menger [2007].
"Next, the empirical background of economic science is definitely inadequate. Our knowledge of the relevant facts of economics is incomparably smaller than that commanded in physics at the time when the mathematization of that subject was achieved. Indeed, the decisive break which came in physics in the seventeenth century, specifically in the field of mechanics, was possible only because of previous developments in astronomy. It was backed by several millennia of systematic, scientific, astronomical observation, culminating in an observer of unparalleled caliber, Tycho de Brahe. Nothing of this sort has occurred in economic science. It would have been absurd in physics to expect Kepler and Newton without Tycho, – and there is no reason to hope for an easier development in economics".
John Von Neumann and Oskar Morgenstern [1970]
The founding fathers of the Austrian school of economics established economic theory on a solid empirical footing in their day, which predetermined its successful development for many years to come. But the current levels of rigor of the underlying concepts and assumptions of these theories, as well as the quantitative description of real economic processes and phenomena, not to mention the quality of economic forecasts, are clearly insufficient for developing an evidence-based management of countries’ economies and achieving sustainable development of the global economy. There is a huge gap between the modern requirements that the society in its wide understanding presents to the economic science and the ability of this science to meet such requirements. This, as 150 years ago, generates a negative, at best ironic, public attitude to economic science, existing in the form of a number of often mutually exclusive theories, such as neoclassical economics and the Austrian school of economics (below often just Austrian economics), whose adherents give contradictory estimates, forecasts and recommendations. It has now come to the realization that empirical foundations alone are clearly insufficient for the verification of adequate models and approaches to economics. It is time to make a strict selection among all existing theories and currents of economic thought by means of their experimental verification in order to further develop economic theory, capable of providing a quantitative description of economic processes and phenomena at a high scientific level, comparable with the level of research in the natural sciences. As a result of this selection, economic theory will get a solid experimental foundation and become a unified economic science, like physics and other natural sciences, rather than a stream of ten parallel currents competing for financial resources, represented by neoclassical economics, Keynesianism, Marxism, etc.
To be clear, let us emphasize once again that all currently wide known economic theories, including neoclassical economics as the mainstream, are essentially heuristic or, at best, empirical theories built upon observation of the economic activities of market agents and the state, as well as on collecting various economic facts and their subsequent verbal generalization into a set of formulated principles for the economic activities of people and enterprises as well as the economic policies of the state. Not surprisingly, therefore, the theories of finance derived from them are extremely limited in their ability to quantitatively describe the temporal fine structure of the dynamics of ordinary and even more so of organized markets both because of our limited knowledge of the general economic laws governing the functioning of markets and because of an almost complete lack of a mathematical body which could be used to calculate at the microscopic level the temporal fine structure of markets in small time intervals, such as one trade session, and then to discover new patterns of how the markets work, using detailed comparison of the obtained results with the experimental data.
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