Acknowledgments
The content of the book is a summary of the results of the project "Quantum Finance Investments of EXCELLENCE Investment Company" in Novosibirsk.
Project participants Vitaly Martynovich and Maria Makarkina contributed greatly to the project's success. Thus, the computer platform QUANTUM FINANCE for calculations of exchange structures using the probabilistic economic theory methods was developed by Vitaliy Martynovich and Maria Makarkina and implemented in C#. Maria Makarkina also provided substantial assistance in preparing this monograph for publication. The author sincerely thanks them for the fruitful cooperation for many years.
The author considers it his duty to thank Dmitry Sviridenko, who undertook the important work of the responsible editor of the monograph, and the reviewers of the monograph, Sergey Parinov and Yuri Perevyshin, for the challenging work of reviewing the manuscript with the new theory at a high professional level.
The author is grateful to the Alexander von Humboldt Foundation (Alexander von Humboldt Stiftung), which provided a scholarship that enabled the author many years ago to witness for the first time how developed market economies work and how financial markets function in West Germany.
The author is grateful to Moscow Exchange and Intercontinental Exchange Futures Europe for providing access to historical data and online quotations.
The author is also grateful to the investment companies FINAM and Interactive Brokers for their excellent broker-intermediary functions with the IB and ICE exchanges, respectively.
The author sincerely thanks the first reader of the book manuscript, Konstantin Gluschenko, for critical comments, consideration of which made the material of the book more understandable for readers who hold fundamentally different orthodox economic views.
In conclusion, the author would like to take the opportunity, unfortunately, very late, to pay back some of his old debts.
First, the author would like to thank Vladimir Evstigneev for his informal but very informative and useful review of the authors first paper on probabilistic economic theory in the collection of papers of the Russian Academy of Sciences and State Administration [Kondratenko, 2005] and Ksenia Kondratenko for her help in preparing the manuscript of this paper. Second, the author notes the important role that Professor George Judge of the University of California (Berkeley) played in this research by approving and enthusiastically supporting that very first paper 15 years ago, for which the author is immensely grateful.
Editor-in-chief
DSc in Physics and Mathematics Professor D.I. Sviridenko
Reviewers:
DSc S.I. Parinov
PhD Y.N. Perevyshin
All rights reserved. No part of the book or whole book may be reproduced or transmitted in any form or by any means without the written permission of the author.
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 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.
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 300600 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.