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Magazine Expansión publishes yearly its list of leading 500 top companies in Mexico. Its cumulative probability sales distribution per employee (per capita) exhibits a two-class structure: a quasi-Pareto power-law in the higher part and an exponential in the lower part which is qualitatively similar to income and wealth distributions in many countries of the world. Therefore, we posit that the income in wages and salaries of many Mexican workers is correlated to the sales revenue per employee of their corresponding employer firms. The relatively small number of state-owned enterprises (SOE) in this list is due to the privatization of most of the Mexican SOE during the past decades.

Introducing a finite capital of the shareholders in the Cont–Bouchaud-model leads to a partially realistic wealth distribution for middle positions in the wealth hierarchy. However, the number of poor shareholders is too small and the capitals of the wealthiest ones are too low. Also variation of the simulation time, of the activity and consideration of the fundamentalists' influence does not give data in agreement with reality.

This article summarizes some physics aspects of the market model of Weisbuch and Stauffer, Physica A (2003): How do demand and quality expectation adjust to each other in a buyer dominated market like cinema visits? And how can business cycles be modelled?

A short review is given of some research topics recently developed in the framework of quantitative finance and which can be referred to the effort of adapting methods and technologies of statistical physics to the analysis of economic systems. In particular we emphasize the role of a different, new perspective, in approaching financial problems, originated within the theory of complex systems and based on concepts like universality, scaling and correlation properties. Once applied to the time evolution of prices and volatility, this approach allows for the recognition of long-range and nonlinear effects in financial time series.

The development of Econophysics is studied from the perspective of scientific communication networks. Papers in Econophysics published from 1992 to 2003 are collected. Then a weighted and directed network of scientific communication, including collaboration, citation and personal discussion, is constructed. Its static geometrical properties, including degree distribution, weight distribution, weight per degree, and betweenness centrality, give a nice overall description of the research works. The way we introduced here to measure the weight of connections can be used as a general one to construct weighted network.

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.

In a case study, the exact solution of a self-consistent Langevin equation associated with a nonlinear Fokker–Planck equation is derived. On the basis of this solution, a Monte Carlo simulation scheme for the Langevin equation is proposed. The case study addresses a generalized geometric Brownian walk that describes the collective dynamics of a large set of interacting stocks. Numerical results obtained from the Monte Carlo simulation are compared with analytical solutions derived from the nonlinear Fokker–Planck equation. The power of the Monte Carlo simulation is demonstrated for situations in which analytical solutions are not available.

A brief introduction and overview is given of the complexity that is possible and the challenges its study poses in many-body systems in which spatial dimension is irrelevant and naively one might have expected trivial behaviour.

We study the topological stability of stock market network by investigating the topological robustness, namely the ability of the network to resist structural or topological changes. The stock market network is extracted by minimal spanning tree (MST) and planar maximally filtered graph (PMFG). We find that the specific delisting thresholds of the listed companies exist in both MST and PMFG networks. In comparison with MST, PMFG provides more information and is better for the aim of exploring stock market network’s robustness. The PMFG before the US sub-prime crisis (i.e., from June 2005 to May 2007) has a stronger robustness against the intentional topological damage than the other two sub-periods (i.e., from June 2007 to May 2009 and from June 2009 to May 2011). We also find that the nonfractal property exists in MSTs of S&P 500, i.e., the highly connected nodes link with each other directly, which indicates that the MSTs are vulnerable to the removal of such important nodes. Moreover, the financial institutions and high technology companies are important in maintaining the stability of S&P 500 network.

The latest global financial tsunami and its follow-up global economic recession has uncovered the crucial impact of housing markets on financial and economic systems. The Chinese stock market experienced a marked fall during the global financial tsunami and China’s economy has also slowed down by about 2%–3% when measured in GDP. Nevertheless, the housing markets in diverse Chinese cities seemed to continue the almost nonstop mania for more than 10 years. However, the structure and dynamics of the Chinese housing market are less studied. Here, we perform an extensive study of the Chinese housing market by analyzing 10 representative key cities based on both linear and nonlinear econophysical and econometric methods. We identify a common collective driving force which accounts for 96.5% of the house price growth, indicating very high systemic risk in the Chinese housing market. The 10 key cities can be categorized into clubs and the house prices of the cities in the same club exhibit an evident convergence. These findings from different methods are basically consistent with each other. The identified city clubs are also consistent with the conventional classification of city tiers. The house prices of the first-tier cities grow the fastest and those of the third- and fourth-tier cities rise the slowest, which illustrates the possible presence of a ripple effect in the diffusion of house prices among different cities.

Based on the order flow data of a stock and its warrant, the immediate price impacts of market orders are estimated by two competitive models, the power-law model (PL model) and the logarithmic model (LG model). We find that the PL model is overwhelmingly superior to the LG model, regarding the robustness of the estimated parameters and the accuracy of out-of-sample forecasting. We also find that the price impacts of ask and bid orders are consistent with each other for filled trades, since significant positive correlations are observed between the model parameters of both types of orders. Our findings may provide valuable insights for optimal trade execution.

This work examines the idea of applying the Chapman–Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first-order in the Knudsen parameter which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper, only a particular case related to the evolution of averages in speculative markets is examined.

We study the various sectors of the Bombay Stock Exchange (BSE) for a period of eight years from January 2006–March 2014. Using the data of the daily returns of a period of eight years we investigate the financial cross-correlation co-efficients among the sectors of BSE and Price by Earning (PE) ratio of BSE Sensex. We show that the behavior of these quantities during normal periods and during crisis is very different. We show that the PE ratio shows a particular distinctive trend in the approach to a crash of the financial market and can therefore be used as an indicator of an impending catastrophe. We propose that a model of analysis of crashes in a financial market can be built using two parameters: (i) the PE ratio and (ii) the largest eigenvalue of the cross-correlation matrix.

A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective phenomena where discrete scale invariance plays an important role. Here we investigate two distinct approaches towards the general problem of how to detect log-periodic oscillations in arbitrary time series without prior knowledge of the location of the moveable singularity. We first show that the problem has a definite solution in Fourier space; however, the technique involved requires an unrealistically large signal-to-noise ratio. Then we show that the quadrature signal obtained via analytic continuation onto the imaginary axis, using the Hilbert transform, necessarily retains the log-periodicities found in the original signal. This finding allows the development of a new method of detecting log-periodic oscillations that relies on calculation of the instantaneous phase of the analytic signal. We then illustrate the method by applying it to the stock market crash of 1987 and explore the important role played by positive feedback mechanisms in relation to economic bubble formation, financial crashes, log-periodic dynamics and analytic behavior. Finally, we discuss the relevance of these findings for parametric rather than nonparametric estimation of critical times.

With the growing demand for energy, the importance of oil as a major energy resource is increasingly evident, and trade has become the key to balancing energy supply and demand. We construct the evolving international oil trade network (iOTN) and analyze the structure and evolution characteristics of the network. Meanwhile, we identify different oil market states by applying the sequential clustering method, combined with relevant network indicators. We find an increase in bilateral cooperation among economies in the oil market, closer trade ties and an upward trend in network reciprocity. The iOTN is heterogeneous, and economies with widely differing trade positions are more likely to cooperate. Trade cooperation with significant trade volumes is more irreplaceable and stable. The changes of oil market state in 1990, 2004 and 2014 indicate that major international events significantly impact the structure of energy systems and trade networks. The division of the oil trade market state by sequential clustering can reflect the reality. Our study clarifies the structural attributes of the iOTN, explores the evolution of the oil trade pattern from the network level, and accurately identifies the state changes in the international oil market.

Based on six large empirical data sets, the financial data sequences are decomposed by Empirical Mode Decomposition (EMD) into various quasi-periodic fluctuation modes, including weekly, half-month, seasonal, about-four-years and so on, which may indicate some abnormal return oscillation patterns. The corresponding average periods are calculated by Fast Fourier Transform Algorithm (FFT), about 6 days for the weekly, about 10 days for the half-month, about 60 days for the seasonal and 1020 days or so for the about-four-years. These obtained results show that the mode periods may be universal for different markets.

The dynamic relaxation of the German DAX both before and after a large price-change is investigated. The dynamic behavior is characterized by a power law. At the minutely time scale, the exponent p governing the power-law behavior takes a same value before and after the large price change, while at the daily time scale, it is different. Numerical simulations of an interacting EZ herding model are performed for comparison.

Financial market is a complex system whose characteristic behaviors can be caught in corresponding time series. Analyzing such time series by appropriate methods will aid in making inferences and predictions. Here phase synchronization approach is used for visual pattern recognition of crises. Based on Empirical Mode Decomposition and the Hilbert transform, phase evolution of various rhythmic components exiting in the market is extracted. Then the concept of synchronization can be successfully applied to crises detection. Unlike other approaches, this detection distinguishes crises from normal state according to variations of interaction among rhythmic components. The empirical results mentioned here convince us of the fact that financial crises take place at the time when the adjustment processes of other quasi-periodic oscillations and the trend are out of synchronization. On the contrary, when other rhythmic oscillations can be synchronized with the trend, the market will develop healthily. The presence and duration of synchronization reflect dynamics of financial market. All these results will enlighten people to disclose its reasons and probe methods for controlling its pathological rhythms.

In this paper, we use mutual information to measure the statistical interdependence between 23 industry sectors of Shanghai stock market and construct corresponding correlation network to analyze the shock of 2008 financial crisis on industry sectors. The obtained meaningful facts are as follows. First, such crisis has only a limited impact on leading industries such as Manufacturing, Commercial trade and Machinery & Equipment, which still play an important role in Chinese economy. Second, the crisis badly attacks China's export industries like Electronics, Wood & Furniture and Textile & Clothing. The damage further hurts other industries, and then export industries' influence becomes larger. Third, the crisis adversely impacts the import industries like Petrochemical, Metal & Nonmetal and Pharmaceutical Biotechnology. While due to the stimulation of macroeconomic policies, the influence of crisis on import industries is limited. Similarly, due to relatively strict capital control and the macroeconomic policies stimulating the domestic demand, those industries like Construction, Real Estate and Financial Services are slightly wounded. All these findings suggest that Chinese government should transform from the external demand to the domestic consumption to sustain economic growth.

The stability of portfolio investment in stock market crashes with Markowitz portfolio is investigated by the method of theoretical and empirical simulation. From numerical simulation of the mean escape time (MET), we conclude that: (i) The increasing number $(Np)$ of stocks in Markowitz portfolio induces a maximum in the curve of MET versus the initial position; (ii) A critical value of $Np$ in the behavior of MET versus the long-run variance or amplitude of volatility fluctuations maximumlly enhances the stability of portfolio investment. When $Np$ takes value below the critical value, the increasing $Np$ enhances the stability of portfolio investment, but restrains it when $Np$ takes value above the critical value. In addition, a good agreement of both the MET and probability density functions of returns is found between real data and theoretical results.