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Special Issue "Three Risky Decades: A Time for Econophysics?"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (29 October 2021) | Viewed by 55615

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A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Ryszard Kutner
E-Mail
Guest Editor
Faculty of Physics, University of Warsaw, Pasteur Str. 5, PL-02093 Warsaw, Poland
Interests: statistical physics; physics of complexity; network science; econophysics and sociophysics; physics of life
Prof. Dr. Christophe Schinckus
E-Mail Website
Guest Editor
School of Business, University of the Fraser Valley, 33844 King Road, Abbotsford, BC V2S 7M8, Canada
Interests: finance; econophysics; complex systems; agent-based modeling; Anthropocene
Prof. Dr. H. Eugene Stanley
grade E-Mail Website
Guest Editor
Department of Physics, Boston University, 590 Commonwealth Ave, Boston, MA 02215, USA
Interests: interdisciplinary science; complex systems; econophysics; sociophysics; liquid water; nanoconfined and biological environments; correlations in Alzheimer brain; quantifying fluctuations in noncoding and coding DNA sequences; interbeat intervals of the healthy and diseased heart

Special Issue Information

Dear Colleagues,

There is a good reason for this Special Issue: next year will mark the third decade of a new way of dealing with economics through the lens of a physics-based approach. Since then, there has been an increasing number of publications (included in the Web of Science database) devoted to what is now called econophysics. The origin of this movement are complex and manifold. A possible catalyst for this increase is the famous conference at the Santa Fe Institute in 1987, organized by two Nobel Prize winners—economist Kenneth Arrow and physicist Philip Anderson. The purpose of this event was to see how economics could benefit from physics, computer science, and biology. Econophysics may be related to the ground-breaking work (“Lévy walks and enhanced diffusion in Milan stock exchange”) written by the physicist Rosario N. Mantegna in 1991—this article, considered by many to be the beginning of modern econophysics, showed that we had entered in an era of extreme and rare events as we experience it almost every day. In addition to these potential origins, other important works also contribute to the development of research related to econophysics: among others, one can quote, “Statistical properties of deterministic threshold elements—the case of market price” by H. Takayasu, H. Miura, T. Hirabayashi, K. Hamada in Physica A (1992), or “The Black-Scholes option pricing problem in mathematical finance: Generalization and extensions for a large class of stochastic processes”, by J.-P. Bouchaud and D. Sornette in J. Phys. I France (1994). We have just cited some of these works here, realizing that this is a subjective selection that reflects our point of view. In this Special Issue, all perspectives on econophysics are welcome, even though they might generate controversial discussions or opposite viewpoints. The authors will have the opportunity to put forth their way of presenting and working with econophysics.

The new era evoked above cannot be characterized through the classical Brownian and Gaussian behavior (Wiener process) originally discovered by Louis Bachelier in his dissertation (“Théorie de la Spéculation” in 1900); instead, the statistical characterization of our contemporary world is more in line with a Lévy flight process over multiple timescales identified by Mantegna in his article on the Milan Index mentioned above. In this context, the central limit theorem has been replaced by the Lévy–Khintchine generalized central limit theorem. These findings have been confirmed by later works—see Mantegna-Stanley in Nature (1995). In a short period of time, an avalanche of publications created an apparently impossible bridge between physics and social sciences (especially financial markets). In this Special Issue, eminent scholars have been invited, all of whom have significantly contributed to econophysics. We hope their writings will illustrate and exemplify the history of econophysics, the current trends in the field, as well as its future perspectives. We voluntarily keep open the scope of this Issue leaving to the authors’ decision what they consider to be the milestones of econophysics and how they see its future. We want econophysics to be presented from different points of view, even though these views might be contradictory or sources of internal scientific tensions. Our work “Econophysics and sociophysics: Their milestones & challenges’ in Physica A (2019) can be used as a source of inspiration for the celebration of the development of econophysics. As Guest Editors, we believe that the Special Issue will be scientifically attractive and inspiring. The 30th anniversary is in opportunity to show econophysics as a living and developing field of science related to many other fields. This Special Issue does not aim to be a museum but instead an inspiring collection of writings opening up prospects for the future of the field.

This Special Issue is also a way to present econophysics to the general public and to scholars who are external to the field: its achievements, its challenges, and even the controversial opinions/internal tensions and sometimes contradictions that might have emerged in the field. As Guest Editors, we are keen to show that econophysics is alive and inspiring—especially in the context of the global challenges with which we are faced.

Prof. Dr. Ryszard Kutner
Prof. Dr. Christophe Schinckus
Prof. Dr. H. Eugene Stanley
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • risk
  • correlations, complexity and entropy
  • multiscaling and multifractality
  • extreme rare events
  • superextreme events
  • dynamics of complex networks
  • income and wealth
  • agent-based and order book modeling
  • observational econophysics
  • physical economics
  • macroeconophysics
  • markets
  • banking
  • games

Published Papers (34 papers)

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Editorial

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Editorial
Three Risky Decades: A Time for Econophysics?
Entropy 2022, 24(5), 627; https://doi.org/10.3390/e24050627 - 29 Apr 2022
Cited by 2 | Viewed by 837
Abstract
The Special Issue comes out in the increasing accumulation of negative global tensions in many areas [...] Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Research

Jump to: Editorial, Review, Other

Article
A New Look at Calendar Anomalies: Multifractality and Day-of-the-Week Effect
Entropy 2022, 24(4), 562; https://doi.org/10.3390/e24040562 - 17 Apr 2022
Cited by 1 | Viewed by 1214
Abstract
Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics [...] Read more.
Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns’ multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Asymmetric Relatedness from Partial Correlation
Entropy 2022, 24(3), 365; https://doi.org/10.3390/e24030365 - 03 Mar 2022
Cited by 1 | Viewed by 1749
Abstract
Relatedness is a key concept in economic complexity, since the assessment of the similarity between industrial sectors enables policymakers to design optimal development strategies. However, among the different ways to quantify relatedness, a measure that takes explicitly into account the time correlation structure [...] Read more.
Relatedness is a key concept in economic complexity, since the assessment of the similarity between industrial sectors enables policymakers to design optimal development strategies. However, among the different ways to quantify relatedness, a measure that takes explicitly into account the time correlation structure of exports is still lacking. In this paper, we introduce an asymmetric definition of relatedness by using statistically significant partial correlations between the exports of economic sectors and we apply it to a recently introduced database that integrates the export of physical goods with the export of services. Our asymmetric relatedness is obtained by generalising a recently introduced correlation-filtering algorithm, the partial correlation planar graph, in order to allow its application on multi-sample and multi-variate datasets, and in particular, bipartite temporal networks. The result is a network of economic activities whose links represent the respective influence in terms of temporal correlations; we also compute the statistical confidence of the edges in the network via an adapted bootstrapping procedure. We find that the underlying influence structure of the system leads to the formation of intuitively-related clusters of economic sectors in the network, and to a relatively strong assortative mixing of sectors according to their complexity. Moreover, hub nodes tend to form more robust connections than those in the periphery. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Heterogeneous Criticality in High Frequency Finance: A Phase Transition in Flash Crashes
Entropy 2022, 24(2), 257; https://doi.org/10.3390/e24020257 - 10 Feb 2022
Viewed by 1138
Abstract
Flash crashes in financial markets have become increasingly important, attracting attention from financial regulators, market makers as well as from the media and the broader audience. Systemic risk and the propagation of shocks in financial markets is also a topic of great relevance [...] Read more.
Flash crashes in financial markets have become increasingly important, attracting attention from financial regulators, market makers as well as from the media and the broader audience. Systemic risk and the propagation of shocks in financial markets is also a topic of great relevance that has attracted increasing attention in recent years. In the present work, we bridge the gap between these two topics with an in-depth investigation of the systemic risk structure of co-crashes in high frequency trading. We find that large co-crashes are systemic in their nature and differ from small ones. We demonstrate that there is a phase transition between co-crashes of small and large sizes, where the former involves mostly illiquid stocks, while large and liquid stocks are the most represented and central in the latter. This suggests that systemic effects and shock propagation might be triggered by simultaneous withdrawals or movement of liquidity by HFTs, arbitrageurs and market makers with cross-asset exposures. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models
Entropy 2022, 24(2), 216; https://doi.org/10.3390/e24020216 - 29 Jan 2022
Cited by 1 | Viewed by 1437
Abstract
The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of [...] Read more.
The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Analysis of Individual High-Frequency Traders’ Buy–Sell Order Strategy Based on Multivariate Hawkes Process
Entropy 2022, 24(2), 214; https://doi.org/10.3390/e24020214 - 29 Jan 2022
Viewed by 1668
Abstract
Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track [...] Read more.
Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track the order history of individual HFTs in the USD/JPY forex market to reveal how individual HFTs interact with the order book and what strategies they use to place their limit orders. Specifically, we introduced an 8-dimensional multivariate Hawkes process that included the excitations due to the occurrence of limit orders, cancel orders, and executions in the order book change, and performed maximum likelihood estimations of the limit order processes for 134 HFTs. As a result, we found that the limit order generation processes of 104 of the 134 HFTs were modeled by a multivariate Hawkes process. In this analysis of the EBS market, the HFTs whose strategies were modeled by the Hawkes process were categorized into three groups according to their excitation mechanisms: (1) those excited by executions; (2) those that were excited by the occurrences or cancellations of limit orders; and (3) those that were excited by their own orders. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
On the Mortality of Companies
Entropy 2022, 24(2), 208; https://doi.org/10.3390/e24020208 - 28 Jan 2022
Viewed by 1085
Abstract
Using data from both the US and UK we examine the survival and mortality of companies in both the early stage or start-up and mature phases. The shape of the mortality curve is broadly similar to that of humans. Even small single cellular [...] Read more.
Using data from both the US and UK we examine the survival and mortality of companies in both the early stage or start-up and mature phases. The shape of the mortality curve is broadly similar to that of humans. Even small single cellular organisms such as rotifers have a similar shape. The mortality falls in the early stages in a hyperbolic manner until around 20–30 years when it begins to rise broadly according to the Gompertz exponential law. To explain in simple terms these features we adapt the MinMax model introduced by the authors elsewhere to explain the shape of the human mortality curve. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Learning Your Options: Option-Based Model of Export Readiness and Optimal Export
Entropy 2022, 24(2), 173; https://doi.org/10.3390/e24020173 - 24 Jan 2022
Viewed by 1286
Abstract
In this short note we offer a novel quantitative approach to modeling of early stages of firm’s internalization, namely stages of accumulation of export readiness and their export debut. In particular, we introduce a new model of export readiness and offer an explicit [...] Read more.
In this short note we offer a novel quantitative approach to modeling of early stages of firm’s internalization, namely stages of accumulation of export readiness and their export debut. In particular, we introduce a new model of export readiness and offer an explicit way of how the export readiness can be accounted in the company share price. The model considers export readiness as a non-observable intangible asset that changes a firm’s asset dynamics. This, in the framework of an option-based debt-equity Merton model, affects both the equity and debt of the company. The approach also allows one to define the contribution of export readiness to equity price and to find a self-consistent quantitative solution to the problem of optimal export strategy and the corresponding optimal firm’s capital allocation. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
Article
Multifractal Company Market: An Application to the Stock Market Indices
Entropy 2022, 24(1), 130; https://doi.org/10.3390/e24010130 - 16 Jan 2022
Cited by 1 | Viewed by 816
Abstract
Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical [...] Read more.
Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Economic Freedom: The Top, the Bottom, and the Reality. I. 1997–2007
Entropy 2022, 24(1), 38; https://doi.org/10.3390/e24010038 - 25 Dec 2021
Viewed by 1682
Abstract
We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of Economic Freedom (IEF); the studied periods are 2000–2006 and 1997–2007, respectively, [...] Read more.
We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of Economic Freedom (IEF); the studied periods are 2000–2006 and 1997–2007, respectively, thereby following the Berlin wall collapse, and including 11 September 2001. After discussing EFW index and IEF, in order to compare the indices, one needs to study their overlap in time and space. That leaves 138 countries to be examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points. The data analysis pertains to the rank-size law technique. It is examined whether the distributions obey an exponential or a power law. A correlation with the country’s Gross Domestic Product (GDP), an admittedly major determinant of EF, follows, distinguishing regional aspects, i.e., defining 6 continents. Semi-log plots show that the EFW-rank relationship is exponential for countries of high rank (≥20); overall the log–log plots point to a behaviour close to a power law. In contrast, for the IEF, the overall ranking has an exponential behaviour; but the log–log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10. Moreover, log–log plots of the EFW index relationship to country GDP are characterised by a power law, with a rather stable exponent (γ0.674) as a function of time. In contrast, log–log plots of the IEF relationship with the country’s gross domestic product point to a downward evolutive power law as a function of time. Markedly the two studied indices provide different aspects of EF. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Evolving Network Analysis of S&P500 Components: COVID-19 Influence of Cross-Correlation Network Structure
Entropy 2022, 24(1), 21; https://doi.org/10.3390/e24010021 - 23 Dec 2021
Viewed by 1750
Abstract
The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The [...] Read more.
The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The analysis is performed on a representative set of USA companies—the S&P500 components. Four different network structures are constructed (strong, weak, typically, and significantly connected networks), and the rank entropy, cycle entropy, averaged clustering coefficient, and transitivity evolution are established and discussed. Based on the mentioned structural parameters, four different stages have been distinguished during the COVID-19-induced crisis. The proposed network properties and their applicability to a crisis-distinguishing problem are discussed. Moreover, the optimal time window problem is analysed. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Cryptocurrency Market Consolidation in 2020–2021
Entropy 2021, 23(12), 1674; https://doi.org/10.3390/e23121674 - 13 Dec 2021
Cited by 18 | Viewed by 2639
Abstract
Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on [...] Read more.
Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
What Drives Bitcoin? An Approach from Continuous Local Transfer Entropy and Deep Learning Classification Models
Entropy 2021, 23(12), 1582; https://doi.org/10.3390/e23121582 - 26 Nov 2021
Cited by 7 | Viewed by 1279
Abstract
Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins’ price direction [...] Read more.
Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins’ price direction under the continuous transfer entropy approach as a feature selection criterion. Accordingly, the statistically significant assets in the sense of permutation test on the nearest neighbour estimation of local transfer entropy are used as features or explanatory variables in a deep learning classification model to predict the price direction of bitcoin. The proposed variable selection do not find significative the explanatory power of NASDAQ and Tesla. Under different scenarios and metrics, the best results are obtained using the significant drivers during the pandemic as validation. In the test, the accuracy increased in the post-pandemic scenario of July 2020 to January 2021 without drivers. In other words, our results indicate that in times of high volatility, Bitcoin seems to self-regulate and does not need additional drivers to improve the accuracy of the price direction. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Continuous Time Random Walk with Correlated Waiting Times. The Crucial Role of Inter-Trade Times in Volatility Clustering
Entropy 2021, 23(12), 1576; https://doi.org/10.3390/e23121576 - 26 Nov 2021
Cited by 2 | Viewed by 821
Abstract
In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of [...] Read more.
In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of these types of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are rare in the physics literature. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by assuming that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model, applied to high-frequency stock market data, can successfully describe the slope of decay of the nonlinear autocorrelation function of stock market returns. We achieve this result without imposing any dependence between consecutive price changes. This proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
Entropy 2021, 23(11), 1505; https://doi.org/10.3390/e23111505 - 13 Nov 2021
Viewed by 881
Abstract
In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in [...] Read more.
In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Victory Tax: A Holistic Income Tax System
Entropy 2021, 23(11), 1492; https://doi.org/10.3390/e23111492 - 11 Nov 2021
Viewed by 1246
Abstract
How can an income tax system be designed to exploit human nature and a free market to create a poverty free society, while balancing budgets without disproportional tax burdens? Such a tax system, with universal character, is deduced from the following guiding principles: [...] Read more.
How can an income tax system be designed to exploit human nature and a free market to create a poverty free society, while balancing budgets without disproportional tax burdens? Such a tax system, with universal character, is deduced from the following guiding principles: (1) a single tax rate applies to all income types and levels; (2) the tax rate adjusts to satisfy budget projections; (3) government transfer only supplements the income of households with self-generated income below the poverty line; (4) deductions for basic living expenses, itemized investments and capital losses are allowed; (5) deductions cannot be applied to government transfer. A general framework emerges with three parameters that determine a minimum allowed tax deduction, a maximum allowed itemized deduction, and a maximum deduction defined by income percentage. An income distribution that mimics the United States, and a series of log-normal distributions are considered to quantitatively compare detailed characteristics of this tax system to progressive and flat tax systems. To minimize government dependency while maximizing after-tax income, the effective tax rate (ETR) as a function of income percentile takes the shape of the letter, V, inspiring the name victory tax, where the middle class has the lowest ETR. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash
Entropy 2021, 23(9), 1211; https://doi.org/10.3390/e23091211 - 14 Sep 2021
Cited by 4 | Viewed by 2408
Abstract
In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically [...] Read more.
In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems
Entropy 2021, 23(9), 1125; https://doi.org/10.3390/e23091125 - 29 Aug 2021
Cited by 5 | Viewed by 1446
Abstract
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon [...] Read more.
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Plotting the Words of Econophysics
Entropy 2021, 23(8), 944; https://doi.org/10.3390/e23080944 - 23 Jul 2021
Cited by 1 | Viewed by 1420
Abstract
Text mining is applied to 510 articles on econophysics to reconstruct the lexical evolution of the discipline from 1999 to 2020. The analysis of the relative frequency of the words used in the articles and their “visualization” allow us to draw some conclusions [...] Read more.
Text mining is applied to 510 articles on econophysics to reconstruct the lexical evolution of the discipline from 1999 to 2020. The analysis of the relative frequency of the words used in the articles and their “visualization” allow us to draw some conclusions about the evolution of the discipline. The traditional areas of research, financial markets and distribution of wealth, remain central, but they are flanked by other strands of research—production, currencies, networks—which broaden the discipline by pushing towards a dialectical application of traditional concepts and tools drawn from statistical physics. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
The Stock Market Model with Delayed Information Impact from a Socioeconomic View
Entropy 2021, 23(7), 893; https://doi.org/10.3390/e23070893 - 14 Jul 2021
Cited by 1 | Viewed by 1399
Abstract
Finding the critical factor and possible “Newton’s laws” in financial markets has been an important issue. However, with the development of information and communication technologies, financial models are becoming more realistic but complex, contradicting the objective law “Greatest truths are the simplest.” Therefore, [...] Read more.
Finding the critical factor and possible “Newton’s laws” in financial markets has been an important issue. However, with the development of information and communication technologies, financial models are becoming more realistic but complex, contradicting the objective law “Greatest truths are the simplest.” Therefore, this paper presents an evolutionary model independent of micro features and attempts to discover the most critical factor. In the model, information is the only critical factor, and stock price is the emergence of collective behavior. The statistical properties of the model are significantly similar to the real market. It also explains the correlations of stocks within an industry, which provides a new idea for studying critical factors and core structures in the financial markets. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Financial Return Distributions: Past, Present, and COVID-19
Entropy 2021, 23(7), 884; https://doi.org/10.3390/e23070884 - 12 Jul 2021
Cited by 13 | Viewed by 1970
Abstract
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by [...] Read more.
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Aspects of a Phase Transition in High-Dimensional Random Geometry
Entropy 2021, 23(7), 805; https://doi.org/10.3390/e23070805 - 24 Jun 2021
Viewed by 1220
Abstract
A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current [...] Read more.
A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Are Mobility and COVID-19 Related? A Dynamic Analysis for Portuguese Districts
Entropy 2021, 23(6), 786; https://doi.org/10.3390/e23060786 - 21 Jun 2021
Cited by 9 | Viewed by 2063
Abstract
In this research work, we propose to assess the dynamic correlation between different mobility indices, measured on a daily basis, and the new cases of COVID-19 in the different Portuguese districts. The analysis is based on global correlation measures, which capture linear and [...] Read more.
In this research work, we propose to assess the dynamic correlation between different mobility indices, measured on a daily basis, and the new cases of COVID-19 in the different Portuguese districts. The analysis is based on global correlation measures, which capture linear and non-linear relationships in time series, in a robust and dynamic way, in a period without significant changes of non-pharmacological measures. The results show that mobility in retail and recreation, grocery and pharmacy, and public transport shows a higher correlation with new COVID-19 cases than mobility in parks, workplaces or residences. It should also be noted that this relationship is lower in districts with lower population density, which leads to the need for differentiated confinement policies in order to minimize the impacts of a terrible economic and social crisis. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
A Maximum Entropy Model of Bounded Rational Decision-Making with Prior Beliefs and Market Feedback
Entropy 2021, 23(6), 669; https://doi.org/10.3390/e23060669 - 26 May 2021
Cited by 5 | Viewed by 2556
Abstract
Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian [...] Read more.
Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their information-processing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the Kullblack–Leibler divergence between posterior decisions and prior beliefs. When information acquisition is free, the homo economicus agent is recovered, while in cases when information acquisition becomes costly, agents instead revert to their prior beliefs. The maximum entropy principle is used to infer least biased decisions based upon the notion of Smithian competition formalised within the Quantal Response Statistical Equilibrium framework. The incorporation of prior beliefs into such a framework allowed us to systematically explore the effects of prior beliefs on decision-making in the presence of market feedback, as well as importantly adding a temporal interpretation to the framework. We verified the proposed model using Australian housing market data, showing how the incorporation of prior knowledge alters the resulting agent decisions. Specifically, it allowed for the separation of past beliefs and utility maximisation behaviour of the agent as well as the analysis into the evolution of agent beliefs. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Highway Freight Transportation Diversity of Cities Based on Radiation Models
Entropy 2021, 23(5), 637; https://doi.org/10.3390/e23050637 - 20 May 2021
Cited by 2 | Viewed by 1309
Abstract
Using a unique data set containing about 15.06 million truck transportation records in five months, we investigate the highway freight transportation diversity of 338 Chinese cities based on the truck transportation probability pij from one city to another. The transportation probabilities [...] Read more.
Using a unique data set containing about 15.06 million truck transportation records in five months, we investigate the highway freight transportation diversity of 338 Chinese cities based on the truck transportation probability pij from one city to another. The transportation probabilities are calculated from the radiation model based on the geographic distance and its cost-based version based on the driving distance as the proxy of cost. For each model, we consider both the population and the gross domestic product (GDP), and find quantitatively very similar results. We find that the transportation probabilities have nice power-law tails with the tail exponents close to 0.5 for all the models. The two transportation probabilities in each model fall around the diagonal pij=pji but are often not the same. In addition, the corresponding transportation probabilities calculated from the raw radiation model and the cost-based radiation model also fluctuate around the diagonal pijgeo=pijcost. We calculate four sets of highway truck transportation diversity according to the four sets of transportation probabilities that are found to be close to each other for each city pair. It is found that the population, the gross domestic product, the in-flux, and the out-flux scale as power laws with respect to the transportation diversity in the raw and cost-based radiation models. It implies that a more developed city usually has higher diversity in highway truck transportation, which reflects the fact that a more developed city usually has a more diverse economic structure. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Optimizing Expected Shortfall under an 1 Constraint—An Analytic Approach
Entropy 2021, 23(5), 523; https://doi.org/10.3390/e23050523 - 24 Apr 2021
Viewed by 1458
Abstract
Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N [...] Read more.
Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N is the number of different assets in the portfolio, and T is the length of the available time series. The critical ratio depends on the confidence level α, which means we have a line of critical points on the αr plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an 1 regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e., a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric 1 regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights, and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio r=N/T, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market
Entropy 2021, 23(3), 352; https://doi.org/10.3390/e23030352 - 15 Mar 2021
Cited by 5 | Viewed by 1445
Abstract
Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant [...] Read more.
Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Development of Econophysics: A Biased Account and Perspective from Kolkata
Entropy 2021, 23(2), 254; https://doi.org/10.3390/e23020254 - 23 Feb 2021
Cited by 4 | Viewed by 1712
Abstract
We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical, as well as social, sciences. After a rather detailed storytelling about our endeavors from Kolkata, we give a brief description of the main research [...] Read more.
We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical, as well as social, sciences. After a rather detailed storytelling about our endeavors from Kolkata, we give a brief description of the main research achievements in a simple and non-technical language. We also briefly present, in technical language, a piece of our recent research result. We conclude our paper with a brief perspective. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Article
Neural Networks for Estimating Speculative Attacks Models
Entropy 2021, 23(1), 106; https://doi.org/10.3390/e23010106 - 13 Jan 2021
Cited by 1 | Viewed by 1656
Abstract
Currency crises have been analyzed and modeled over the last few decades. These currency crises develop mainly due to a balance of payments crisis, and in many cases, these crises lead to speculative attacks against the price of the currency. Despite the popularity [...] Read more.
Currency crises have been analyzed and modeled over the last few decades. These currency crises develop mainly due to a balance of payments crisis, and in many cases, these crises lead to speculative attacks against the price of the currency. Despite the popularity of these models, they are currently shown as models with low estimation precision. In the present study, estimates are made with first- and second-generation speculative attack models using neural network methods. The results conclude that the Quantum-Inspired Neural Network and Deep Neural Decision Trees methodologies are shown to be the most accurate, with results around 90% accuracy. These results exceed the estimates made with Ordinary Least Squares, the usual estimation method for speculative attack models. In addition, the time required for the estimation is less for neural network methods than for Ordinary Least Squares. These results can be of great importance for public and financial institutions when anticipating speculative pressures on currencies that are in price crisis in the markets. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Review

Jump to: Editorial, Research, Other

Review
Valuing the Future and Discounting in Random Environments: A Review
Entropy 2022, 24(4), 496; https://doi.org/10.3390/e24040496 - 01 Apr 2022
Cited by 1 | Viewed by 1032
Abstract
We address the process of discounting in random environments, which allows valuation of the future in economic terms. We review several approaches to the problem regarding different well-established stochastic market dynamics in the continuous-time context and include the Feynman–Kac approach. We also review [...] Read more.
We address the process of discounting in random environments, which allows valuation of the future in economic terms. We review several approaches to the problem regarding different well-established stochastic market dynamics in the continuous-time context and include the Feynman–Kac approach. We also review the relation between bond-pricing theory and discounting and introduce both the market price of risk and the risk neutral measure from an intuitive point of view devoid of excessive formalism. We provide the discount for each economic model and discuss their key results. We finally present a summary of our previous empirical studies for several countries on the long-run discount problem. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Review
Three Decades in Econophysics—From Microscopic Modelling to Macroscopic Complexity and Back
Entropy 2022, 24(2), 271; https://doi.org/10.3390/e24020271 - 14 Feb 2022
Cited by 1 | Viewed by 2227
Abstract
We explore recent contributions to research in Econophysics, switching between Macroscopic complexity and microscopic modelling, showing how each leads to the other and detailing the everyday applicability of both approaches and the tools they help develop. Over the past decades, the world underwent [...] Read more.
We explore recent contributions to research in Econophysics, switching between Macroscopic complexity and microscopic modelling, showing how each leads to the other and detailing the everyday applicability of both approaches and the tools they help develop. Over the past decades, the world underwent several major crises, leading to significant increase in interdependence and, thus, complexity. We show here that from the perspective of network science, these processes become more understandable and, to some extent, also controllable. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Review
Econophysics and the Entropic Foundations of Economics
Entropy 2021, 23(10), 1286; https://doi.org/10.3390/e23101286 - 30 Sep 2021
Cited by 5 | Viewed by 1609
Abstract
This paper examines relations between econophysics and the law of entropy as foundations of economic phenomena. Ontological entropy, where actual thermodynamic processes are involved in the flow of energy from the Sun through the biosphere and economy, is distinguished from metaphorical entropy, where [...] Read more.
This paper examines relations between econophysics and the law of entropy as foundations of economic phenomena. Ontological entropy, where actual thermodynamic processes are involved in the flow of energy from the Sun through the biosphere and economy, is distinguished from metaphorical entropy, where similar mathematics used for modeling entropy is employed to model economic phenomena. Areas considered include general equilibrium theory, growth theory, business cycles, ecological economics, urban–regional economics, income and wealth distribution, and financial market dynamics. The power-law distributions studied by econophysicists can reflect anti-entropic forces is emphasized to show how entropic and anti-entropic forces can interact to drive economic dynamics, such as in the interaction between business cycles, financial markets, and income distributions. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Review
Energy, Entropy, Constraints, and Creativity in Economic Growth and Crises
Entropy 2020, 22(10), 1156; https://doi.org/10.3390/e22101156 - 14 Oct 2020
Cited by 3 | Viewed by 1911
Abstract
The neoclassical mainstream theory of economic growth does not care about the First and the Second Law of Thermodynamics. It usually considers only capital and labor as the factors that produce the wealth of modern industrial economies. If energy is taken into account [...] Read more.
The neoclassical mainstream theory of economic growth does not care about the First and the Second Law of Thermodynamics. It usually considers only capital and labor as the factors that produce the wealth of modern industrial economies. If energy is taken into account as a factor of production, its economic weight, that is its output elasticity, is assigned a meager magnitude of roughly 5 percent, according to the neoclassical cost-share theorem. Because of that, neoclassical economics has the problems of the “Solow Residual”, which is the big difference between observed and computed economic growth, and of the failure to explain the economic recessions since World War 2 by the variations of the production factors. Having recalled these problems, we point out that technological constraints on factor combinations have been overlooked in the derivation of the cost-share theorem. Biophysical analyses of economic growth that disregard this theorem and mend the neoclassical deficiencies are sketched. They show that energy’s output elasticity is much larger than its cost share and elucidate the existence of bidirectional causality between energy conversion and economic growth. This helps to understand how economic crises have been triggered and overcome by supply-side and demand-side actions. Human creativity changes the state of economic systems. We discuss the challenges to it by the risks from politics and markets in conjunction with energy sources and technologies, and by the constraints that the emissions of particles and heat from entropy production impose on industrial growth in the biosphere. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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Other

Perspective
Radical Complexity
Entropy 2021, 23(12), 1676; https://doi.org/10.3390/e23121676 - 14 Dec 2021
Viewed by 1714
Abstract
This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps [...] Read more.
This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined. Full article
(This article belongs to the Special Issue Three Risky Decades: A Time for Econophysics?)
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