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Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years before a new firm emerges and rapidly obtains a large market share. We seek the simplest realistic model giving rise to such diverse market structures and dynamics. We focus on markets in which every client adopts a single firm, and can, from time to time, switch to a different firm. Examples include markets of cell phone and Internet service providers, and of consumer products with strong brand identification. In the model, the size of a particular firm, labelled i , is equal to its current number of clients, n i. In every step of the simulation, a client is chosen at random, and then selects a firm from among the full set of firms with probability p i = (n i α + β) / K , where K is the normalization factor. Our model thus has two parameters: α represents the degree to which firm size is an advantage (α > 1) or disadvantage (α < 1), relative to strict proportionality to size (α = 1), and β represents the degree to which small firms are viable despite their small size. We postulate that α and β are determined by the regulatory, technology, business culture and social environments. The model exhibits a phase diagram in the parameter space, with different regions of behaviour. At the large α extreme of the phase diagram, a single dominant firm emerges, whose market share depends on the value of β. At the small α extreme, many firms with small market shares coexist, and no dominant firm emerges. In the intermediate region, markets are divided among a relatively small number of firms, each with sizeable market share but with distinct rankings, which can persist for long times before changing. We compare the model results to previously published empirical data from a broad range of Japanese industries, and find good agreement with a central statistical result relating the standard deviation of market share changes to the value of the market share before the change. • Two-parameter model of market structure evolution based on client switching. • Each individual client has a single firm, and can change firms from time to time. • Produces full range of market concentrations, from monopoly to many small firms. • Model results are consistent with empirical data from range of Japanese markets. [ABSTRACT FROM AUTHOR]

Previous research explored various conditions of financial markets based on the similarity of correlation structures and classified as market states. We introduce modifications to previous selection criteria for these market states, mainly due to increased attention to the transition matrix between the states. Clustering and thus market states are fixed by the optimization of two parameters — number of clusters and noise-suppression, but in similar conditions, we give preference to the clustering which avoids large jumps in the transition matrix. We found statistically significant results applying this model to the S&P 500 and Nikkei 225 markets for the pre-COVID-19 pandemic era (2006–2019). Retaining the epoch length of 20 trading days but reducing the shift of the epoch to a single trading day we are led to the concept of a trajectory of the market in the space of correlation matrices. We may visualize these states after dimensional scaling to two or three dimensions. This approach, using dynamics, improves the options of risk assessment, opens the door to dynamical treatments of markets (e.g. hedging), and shows noise-suppression in a new light. • Financial markets dynamics in the space of correlation matrices are analyzed. • An improved technique to obtain market states is proposed. • Trajectories of the market in the space of correlation matrices are visualized. [ABSTRACT FROM AUTHOR]

This paper extends the recent work of Shibata from static perspective to dynamic perspective, presents a differential game model of pollution abatement R&D investment with emission tax. Two key factors to continuously measuring the intensity of market competition and pollution abatement R&D investment spillovers respectively are included in the model. Results show that before the termination point of the project, as the market becomes more competitive, noncooperative R&D investment is more likely to be preferred. There are cases in which, contrary to conventional wisdom, when the market is perfectly competitive, the cooperative pollution abatement R&D investment is zero but the noncooperative investment is not zero; the pollution abatement R&D investment spillovers have some positive influence on optimal cooperative R&D investment while make the optimal noncooperative R&D investment decrease. • Two key factors to continuously measuring the intensity of market competition and pollution abatement R&D investment spillovers respectively are included in the model. • We investigate the optimal strategies under cooperative and noncooperative game. • The effects of parameters on the results are examined. • The pollution abatement R&D investment spillovers have some positive influence on optimal cooperative R&D investment while make the optimal noncooperative R&D investment decrease. [ABSTRACT FROM AUTHOR]

Partial correlation analysis is employed to study the market impact on the Chinese stock market from both the native and external markets. Whereas the native market index is observed to have a great impact on the market correlations for both the Shanghai and Shenzhen stock markets, some external stock indices of the United States, European and Asian stock markets show a slight influence on the Chinese market. The individual stock can be affected by different economic sectors, but the dominant influence is from the sector the stock itself belongs to or closely related to, and the finance and insurance sector shows a weaker correlation with other economic sectors. Moreover, the market structure similarity exhibits a negative correlation with the price return in most time, and the structure similarity decays with the time interval. [ABSTRACT FROM AUTHOR]

We study how to assess the potential benefit of diversifying an equity portfolio by investing within and across equity sectors. We analyse 20 years of US stock price data, which includes the global financial crisis (GFC) and the COVID-19 market crash, as well as periods of financial stability, to determine the 'all weather' nature of equity portfolios. We establish that one may use the leading eigenvalue of the cross-correlation matrix of log returns as well as graph-theoretic diagnostics such as modularity to quantify the collective behaviour of the market or a subset of it. We confirm that financial crises are characterised by a high degree of collective behaviour of equities, whereas periods of financial stability exhibit less collective behaviour. We argue that during times of increased collective behaviour, risk reduction via sector-based portfolio diversification is ineffective. Using the degree of collectivity as a proxy for the benefit of diversification, we perform an extensive sampling of equity portfolios to confirm the old financial adage that 30–40 stocks provide sufficient diversification. Using hierarchical clustering, we discover a 'best value' equity portfolio for diversification consisting of 36 equities sampled uniformly from 9 sectors. We further show that it is typically more beneficial to diversify across sectors rather than within. Our findings have implications for cost-conscious retail investors seeking broad diversification across equity markets. • We analyse 20 years of US daily stock price data. • PCA and graph theoretic diagnostics quantify the degree of financial market collectivity. • A new sampling procedure compares diversification within and across equity sectors. • A best-value portfolio consisting of 36 equities from 9 sectors is found. • Our portfolio diversification findings may provide cheap diversification for retail investors. [ABSTRACT FROM AUTHOR]

Based on empirical properties of the global phonographic market, we propose a simple epidemiological model of innovation spread on a network whose structure reflects the structure of the real-world market. The global phonographic market consists of the national markets of various size and mutual interconnections. In the model, we assume that the national markets are the subnetworks that have a scale-free structure achieved by the preferential attachment construction with a node hierarchy and binary edges, while the global market is a complete, directed, weighted network of these subnetworks treated as nodes with the edges representing the cultural and geographical proximity of the national markets. "Viruses" with a defined strength or aggressiveness occur independently at one of the nodes of a selected subnetwork and correspond to a piece of music that has been released by an artist somewhere in the world. We study the virus dynamics set by varying parameter values and observe a variety of phenomena including local and global pandemics and the existence of an epidemic threshold in the subnetworks. Apart from studying the model, we also present some results on empirical data from the European and the U.K. phonographic markets, which are then utilized in the model construction. • Global phonographic market can be represented by epidemiological model of popularity spread. • The global market is divided into cultural clusters of national markets. • Hit popularity depends on commercial potential, origin, and infection persistence. • Only a few hit singles are able to affect the entire global market. • Hit's global success is more likely after its success on a domestic market. [ABSTRACT FROM AUTHOR]

Many emerging cryptocurrencies make it important to analyze the evolution of correlations in the cryptocurrency market. This paper uses a network method to identify critical events in the correlation dynamics of cryptocurrencies. We use the influence strength (I S) as an indicator to describe the level of change caused by critical events. The empirical analysis shows huge fluctuations in the market index near the critical event, indicating a relationship between the correlation matrix dynamics and market states. In addition, we find a synchronization between changes in correlation and changes in network structure; a positive correlation is observed. Finally, we take the networks around January 6, 2021 as an example to show local and drastic changes in the correlation structure. This paper analyzes the stability and fragility of the correlation structure in the cryptocurrency market, which helps to analyze the dynamics of this emerging market. • The correlation dynamics of cryptocurrencies includes some critical events. • Critical events are related to market fluctuations. • IS-based analysis is used to analyze the dynamics of correlation networks. • The network structure is easy to be destroyed near some critical times. [ABSTRACT FROM AUTHOR]

This paper introduces new methods for analysing the extreme and erratic behaviour of time series to evaluate the impact of COVID-19 on cryptocurrency market dynamics. Across 51 cryptocurrencies, we examine extreme behaviour through a study of distribution extremities, and erratic behaviour through structural breaks. First, we analyse the structure of the market as a whole and observe a reduction in self-similarity as a result of COVID-19, particularly with respect to structural breaks in variance. Second, we compare and contrast these two behaviours, and identify individual anomalous cryptocurrencies. Tether (USDT) and TrueUSD (TUSD) are consistent outliers with respect to their returns, while Holo (HOT), NEXO (NEXO), Maker (MKR) and NEM (XEM) are frequently observed as anomalous with respect to both behaviours and time. Even among a market known as consistently volatile, this identifies individual cryptocurrencies that behave most irregularly in their extreme and erratic behaviour and shows these were more affected during the COVID-19 market crisis. • This paper analyses the 51 largest cryptocurrencies by market capitalisation. • We introduce new methods of analysis of extreme and erratic behaviour of time series. • Hierarchical clustering of extremal distributions and change points is applied. • Inconsistency matrices between these behaviours and time periods are introduced. • Anomalous cryptocurrencies with respect to behaviour and time are identified. [ABSTRACT FROM AUTHOR]

The financial market dynamics has been widely studied by theoretical methods developed in turbulence. The hierarchical structure of stock market related to multifractal scaling has been found by She–Leveque (SL) hierarchy theory. In this paper, we further quantitatively investigate the universal and nonuniversal properties of such hierarchical structure based on diverse price indices and sector indices in various stock markets. Meanwhile, we consider the sampling duration of these indices spanning 6 fiscal years from 2006 to 2011, and mainly investigate the impact of subprime mortgage crisis on the hierarchical structure of stock market. In the perspective of price index and sector index, the empirical results show that the hierarchical structure is universal and generic to stock market dynamics, but its degree is nonuniversal in restricted to different scaling exponent β among the stock markets or sectors. We understand that the nonuniversal degrees of hierarchical structure are induced by the imbalance of state or sector economic development. More importantly, we comprehensively analyze the evolution of β in respect to each fiscal year to understand the impact of global financial crisis on the stock market dynamics. In the perspective of price index, we find the evolutionary trends of β are different between Euramerican and Asian regions, and the deviations of β in the fiscal year 2007 and 2008 are much smaller. Also, in the perspective of sector index, similar results are unveiled that the deviation of β is the smallest in the fiscal year 2008. These empirical results based on the evolution of β to some extent imply the great impact of global financial crisis on the collective dynamics of stock markets. • The stock market dynamics is investigated by SL hierarchy theory. • The hierarchical structure of stock market is universal. • The degree of hierarchical structure is different for various stock markets. • The hierarchical structure is significantly impacted by the global financial crisis. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of multifractal structure of the eight historical Chinese stock market crashes based on the Shanghai Stock Exchange Composite Index (SSECI). It supports that the multifractal dimension describes well the behavior of self-organized criticality of the eight crashes, suggesting that the multifractal dimension is available to predict the crash. We also attempt to analyze the impact of policy and market institutional structure on the crashes, proposing that the stock market conditions have a great impact on the fractal dimension of stock crashes: A strong government intervention in the stock market corresponds to a low fractal dimension and high intensity crash, and vice versa. • A multifractal structure for the eight Chinese stock crashes are detected well. • A strong intervention corresponds to a low fractal dimension and high intensity crash. • The general multifractal dimension can be used for advanced warning of a stock crash. [ABSTRACT FROM AUTHOR]

We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson–Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-sets representing any two distributions. The degree to which different entities, (markets, universities, hospitals, cities, groups of securities, etc.), have different distance measures of their corresponding distributions tells us the extent to which they are different, aiding participants looking for diversification or looking for more of the same thing. We demonstrate a relationship between covariance and distance measures based on a generic extension of Stein's Lemma. We consider an asset pricing application and then briefly discuss how this methodology lends itself to numerous market–structure studies and even applications outside the realm of finance / social sciences by illustrating a biological application. We provide numerical illustrations using security prices, volumes and volatilities of both these variables from six different countries. • Novel methodology combining Bhattacharyya distance and Johnson–Lindenstrauss Lemma. • Powerful tool allowing comparisons between data representing any two distributions. • Demonstration of a relationship between covariance and distance measures. • Discussion of asset pricing, market structure and biological applications. • Numerical illustrations using financial market data from six different countries. [ABSTRACT FROM AUTHOR]

We demonstrate that future market correlation structure can be predicted with high out-of-sample accuracy using a multiplex network approach that combines information from social media and financial data. Market structure is measured by quantifying the co-movement of asset prices returns, while social structure is measured as the co-movement of social media opinion on those same assets. Predictions are obtained with a simple model that uses link persistence and link formation by triadic closure across both financial and social media layers. Results demonstrate that the proposed model can predict future market structure with up to a 40% out-of-sample performance improvement compared to a benchmark model that assumes a time-invariant financial correlation structure. Social media information leads to improved models for all settings tested, particularly in the long-term prediction of financial market structure. Surprisingly, financial market structure exhibited a higher predictability than social opinion structure. • Social opinion structure is relevant to predict stock market correlation structure. • Proposed model improves market structure predictions in up to 40%. • Social media leads to improved models particularly in long-term predictions. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that emerging stock markets and mature stock markets differ in many respects, while research on emerging markets is rather insufficient compared to well-studied mature markets. In this paper, we investigate the unique network properties and market pattern of the emerging Chinese stock market of crude oil related companies with the implementation of minimum spanning trees(MST) and hierarchical trees(HT). For a robust quantification of cross-correlation between stocks, detrended cross-correlation coefficient (DCCA coefficient) and partial cross-correlation coefficient (DPXA coefficient) are applied to reveal the overall cross-correlation and identify the common external factor on price fluctuations respectively. The paper depicts the dynamic evolution of Chinese stock market of crude oil related companies, showing the variation of structural density and stability under different time scales and market environments. The establishment of correlation-based networks provides a more pertinent explanation for the unusual market structure and conduct of the emerging Chinese stock market, contributing to both portfolio decisions and risk resistance. • Network properties and market patterns of the emerging Chinese stock market of crude oil related companies are explored by MST and HT. • DCCA coefficient and DPXA coefficient are applied respectively. • Small-volume stocks capture hub positions more frequently in both upturn and recession periods. [ABSTRACT FROM AUTHOR]

The purpose of this research is to analyze the structure of the cryptocurrency market based on the correlation-based agglomerative hierarchical clustering and minimum spanning tree. In order to detect a reasonable and distinct collective behavior among the market entities, we propose a filtering mechanism, called Bitcoin–Ethereum filtering, to exclude their linear influences to other cryptocurrencies. In this regard, we carefully examine the market structures for the cases of before and after filtering in terms of the Total, Pre-, and Post-regulation periods. Based on the results, we discover the leadership of the Bitcoin and Ethereum in the market, six homogeneous clusters composed of relatively less-traded cryptocurrencies, and transformation of the market structure after the announcement of regulations from various countries. • Structure of the cryptocurrency market is analyzed via Bitcoin–Ethereum filtering. • Agglomerative hierarchical clustering and minimum spanning tree analyses are applied. • Market leadership of the Bitcoin and Ethereum are established. • Six homogeneous clusters composed of less traded cryptocurrencies are detected. • Market structure is transformed after the announcements of various regulations. [ABSTRACT FROM AUTHOR]