Econophysics is a branch of economics that applies concepts and methods from physics to the financial markets. This article focuses on the approaches to quantum finance developed by Kirill Ilinski and Belal E. Baaquie to deal with the uncertainty characterizing financial time series. Allegedly, their models rest on a formal analogy between quantum mechanics and finance. In order to evaluate them, we raise the question what is really quantum in quantum econophysics. We then argue that the supposed analogy breaks in an important manner, which is relevant to explain the empirical success of the proposed models.
Econophysics is a branch of economics that applies concepts and methods from physics to the financial markets. This article focuses on the approaches to quantum finance developed by Kirill Ilinski and Belal E. Baaquie to deal with the uncertainty characterizing financial time series. Allegedly, their models rest on a formal analogy between quantum mechanics and finance. In order to evaluate them, we raise the question what is really quantum in quantum econophysics. We then argue that the supposed analogy breaks in an important manner, which is relevant to explain the empirical success of the proposed models.
Approaching physics as the way to predict the results of experiments is good enough for physics as it is. However the transition of its notions and mathematical apparatus to systems of different nature requires obligatory in-depth analysis of its initial concepts. Econophysics is a young interdisciplinary scientific field, which developed and acquired its name at the end of the last century. Quantum econophysics, a direction distinguished by the use of mathematical apparatus of quantum mechanics as well as its fundamental conceptual ideas and relativistic aspects, developed within its boundaries just a couple of years later, in the first decade of the 21-st century. In this paper from quantum econophysics positions, attained by moderntheoretical physics in understanding of the universe bases, the methodological and philosophicalanalysis of fundamental physical concepts and their formal and informal connections with thereal economic measurings is carried out. The possibility of introducing economic equivalents ofphysical quantities in order to describe socio-economic processes using the quantum uncertaintyprinciple is shown. Procedures for heterogeneous economic time determination, normalizedeconomic coordinates and economic mass are offered, based on the analysis of time series, theconcept of economic Plank's constant is proposed. A theory is approved on the real economicdynamic's time series, including crises stock market indices. It is shown that the effective mass ofthe time series universally decreases before the crisis period, which may be an indicator of thecrisis phenomena.
The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance has produced valuable results. The principal movement which has steered this research direction is known under the name of `econophysics'. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under `uncertainty' in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as `quantum probability') enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.
Classical and Quantum Physics in Selected Economic Models A growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win. The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.
Introduction. Modern financial science increasingly faces a paradox: classical models based on deterministic assumptions fail to adequately describe the nonlinearity and uncertainty of public decision-making. In this context, the quantum paradigm of thinking, originally developed in physics, is becoming increasingly relevant as it gradually penetrates the fields of economics and finance. Problem Statement. In contemporary academic discourse, growing attention is being paid to the integration of the principles of quantum logic into socio-economic systems. Traditional financial science rests upon classical macroeconomic determinants that assume linearity, causal determinacy, and parameter stability. However, in the modern world – characterized by high uncertainty, dynamic crises, and global financial fluctuations – such logic proves insufficient. Therefore, there is a pressing need to employ quantum logic as a modern cognitive and analytical paradigm that enables the comprehension of the essence and structure of public finance through the prism of nonlinear, stochastic, and interrelated phenomena and processes. Purpose is to establish a theoretical and methodological foundation for applying quantum principles in the domain of public finance and to identify directions for their practical implementation. Methods. To obtain the scientific results presented in the article, the following methods were employed: methods of quantum logic, synthesis and analysis, deduction and induction, an abstract-logical method of “negation of negations” in financial decision-making, and theoretical generalization to define the nature of quantum finance. Results. The article reveals the potential for interpreting key principles of quantum physics within the system of public finance. A dual-level research framework is proposed, combining methodological analogies between quantum and financial processes with the practical application of quantum models in state financial management. It is demonstrated that the concepts of uncertainty, superposition, and coherence allow for a deeper understanding of the nature of budgetary decisions, tax expectations, debt imbalances, and behavioral effects in the public sphere. Conclusions. Quantum logic crystallizes a methodological framework for modern public finance capable of accounting for the complexity, uncertainty, and interconnectivity of global transformations, hybrid wars, and the contemporary economy. The application of quantum paradigms makes it possible to construct dynamic, probabilistic models of financial policy that significantly surpass the capacities of classical deterministic methods and open new perspectives for scientifically grounded public governance in the field of public finance.
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study the possibility of application of the quantum probabilistic model to agents of financial market. We show that, although the direct quantum (physical) reduction (based on using the scales of quantum mechanics) is meaningless, one may apply so called quantum-like models. In our approach quantum-like probabilistic behaviour is a consequence of contextualy of statistical data in finances (and economics in general). However, our hypothesis on "quantumness" of financial data should be tested experimentally (as opposed to the conventional description based on the noncontextual classical probabilistic approach). We present a new statistical test based on a generalization of the well known in quantum physics Bell's inequality.
This concise and self-contained book opens completely novel areas of research by directly implementing concepts from quantum physics into areas of social science. It constructs compelling arguments originating from fundamental concepts in physics and the philosophy of science, including key developments in economics and finance, then surveys the important work which has been performed to date through applying the formalism of quantum mechanics to decision making and finance. The book is accessible to graduate students and researchers in social science and physics, as well as avid interdisciplinary readers. This title is part of the Flip it Open Programme and may also be available Open Access. Check our website Cambridge Core for details.