The paper aims at analyzing the dynamics of the core-periphery structure of tail risk dependence among 221 cryptocurrencies in the period Jan. 1st, 2022-Nov. 21st, 2025. From a methodological perspective, the paper proposes an integrated framework that combines breakpoint detection, CoVaR estimation, dynamic network construction, and spectral core periphery analysis to study the transmission of systemic tail risk in cryptocurrency markets. While most existing studies focus on static dependence structures, pairwise spillovers, or traditional centrality measures, our approach allows us to track how the core periphery structure changes over time and across different market regimes. From a theoretical point of view, the paper contributes to a better understanding of how systemic importance evolves in cryptocurrency markets. Our findings show that the market does not change gradually, but rather moves through distinct structural phases, each characterized by a different configuration of core and peripheral assets. The results point out that, across all periods, the core tends to follow a recurring pattern of expansion, consolidation, peak, and divergence. This highlights how the role of cryptocurrencies within the overall risk structure changes over time, with some assets becoming more central during periods of market stress and others moving back to the periphery. Identifying the cryptocurrencies that consistently belong to the core can be useful for risk management, since these assets are more likely to spread shocks during periods of market stress. Distinguishing between core and peripheral assets may also help investors identify better diversification opportunities, while from a regulatory perspective it may support the monitoring of cryptocurrencies that are becoming increasingly important for overall market stability.

We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are presented in the context of applied problems to visualise the strengths and drawbacks of the approach. The major aim of capturing such a broad overview is to understand the interrelations between network theories that seem to be distant from the mathematical perspective.

This work proposes a hybrid model that combines the Galam model of opinion dynamics with the Bass diffusion model used in technology adoption on Barabasi–Albert complex networks. The main idea is to advance a version of the Bass model that can suitably describe an opinion formation context while introducing irreversible transitions from group B (opponents) to group A (supporters). Moreover, we extend the model to take into account the presence of a charismatic competitor, which fosters conversion back to the old technology. The approach is different from the introduction of a mean field due to the interactions driven by the network structure. Additionally, we introduce the Kolmogorov–Sinai entropy to quantify the system’s unpredictability and information loss over time. The results show an increase in the regularity of the trajectories as the preferential attachment parameter increases.

Targeting systemic risk, we propose a two-stage analysis of a large collection of stock markets by considering their interconnections. First, we characterize the joint dynamics of stock returns using a multivariate GARCH model in the presence of regime changes. The model detects three regimes of volatility rising from two unknown but common endogenous breaks. We compute filtered returns by normalizing them using the dynamic GARCH volatility. Second, we build a Gaussian signed weighted and undirected worldwide financial network from filtered stock returns, that evolves across regimes. The best network is built from the partial correlation matrix of filtered stock returns over each regime using regularisation and the minimum Extended Bayesian Information Criterion. To gain insights into the resilience of the financial network and its systemic risk over time, we then compute relevant nodal centrality measures—including the clustering coefficient—over each regime. Thus, we characterize the ever-changing network topology and structure by detecting group-like and community-like patterns (e.g., clustering and community detection, network cohesion). Under the resilience framework and depending on the studied regime, we analyse the propensity of a shock to propagate across the network thanks to positive weights, and the network’s ability to mitigate shocks thanks to negative weights. The balance between spreading and inhibiting node influences drives the network’s frailty and resilience to shocks. Hence, the network exhibits a high level of systemic risk when its connectivity is large and most edge weights are significantly positive (i.e., strong and multiple conditional dependencies of world stock markets). It is of high significance to policymakers because systemic risk/financial frailty is potentially costly (i.e., loss) while resilience is rewarding (i.e., gain).

The term "Fintech" refers to the use of technology to automate various financial services, products, and operations. The aim of this paper is to examine the patents certificates to analyze technology trends and to forecast future developments related to the various aspects of Fintech. Through the network analysis of the patent dataset, we identified five relevant technological clusters that allowed us to detect the technological substrate underlying the corresponding cluster. The Bass diffusion model permitted the observation of the technological trajectories of each cluster outlining the diffusion patterns.

In this study, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow for the ranking of “agents”, “opinions”, etc., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to specify the framework, we discuss previous attempts, recalling trivial means of scores—weighted or not—Condorcet paradox, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), etc. We demonstrate, through geometrical arguments on a toy example and with four criteria, that the pre-selected order of criteria in previous attempts makes a difference in the final result. However, it might be unjustified. Thus, we base our “best choice theory” on the linear response theory in statistical physics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with six possible criteria. Applications in many fields are suggested. Furthermore, two toy models, serving as practical examples and illustrative arguments are discussed.

Patents are important sources of technical knowledge because they offer a wealth of information on innovations and technological developments. This paper focuses on Fintech-related patent certificates in order to examine the technical trends in this particular sector and discuss the factors influencing technological advancement. The data were retrieved through the World Intellectual Property Organization database, considering selected keywords. Through the network analysis, we identify five relevant technological clusters that allow us to detect the technological substrate underlying the corresponding cluster. The Bass diffusion model permits the observation of the technological trajectories of each cluster, outlining the diffusion patterns. Furthermore, particular attention is given to the developing technologies defined as "green", and we describe how these trends have changed over time and predict their future technological trajectory. Our findings provide an in-depth analysis of the Fintech patent landscape, highlighting the connections between the different technologies. It also allows us to assess the technological leadership of companies and the technological life cycle that describes the diffusion patterns.

Political events play a significant role in exerting their influence on financial markets globally. This paper aims to investigate the long term effect of Brexit on European stock markets using Complex Network methods as a starting point. The media has heavily emphasized the connection between this major political event and its economic and financial impact. To analyse this, we created two samples of companies based on the geographical allocation of their revenues to the UK. The first sample consists of companies that are either British or financially linked to the United Kingdom. The second sample serves as a control group and includes other European companies that are conveniently matched in terms of economic sector and firm size to those in the first sample. Each analysis is repeated over three non-overlapping periods: before the 2016 Referendum, between the Referendum and the 2019 General Elections, and after the 2019 General Elections. After an event study aimed at verifying the short-term response of idiosyncratic daily returns to the referendum result, we analysed the topological evolution of the networks through the MST (Minimum Spanning Trees) of the various samples. Finally, after the computation of the centrality measures pertaining to each network, our attention was directed towards the examination of the persistence of the levels of degree and eigenvector centralities over time. Our target was the investigation on whether the events that determined the evolution of the MST had also brought about structural modifications to the centrality of the most connected companies within the network. The findings demonstrate the unexpected impact of the referendum outcome, which is more noticeable on European equities compared to those of the UK, and the lack of influence from the elections that marked the beginning of the hard Brexit phase in 2019. The modifications in the MST indicate a restructuring of the network of British companies, particularly evident in the third period with a repositioning of the UK nodes. The dynamics of the MSTs around the referendum date is associated with the persistence in the relative rank of the centrality measures (relative to the median). Conversely, the arrival of hard Brexit does alter the relative ranking of the nodes in accord to the the degree centrality. The ranking in accord to the eigenvector centrality keeps the persistence. However, such movements are not statistically significant. An analysis of this kind points out relevant insights for investors, as it equips them to have a comprehensive view of political events, while also assisting policymakers in their endeavour to uphold stability by closely monitoring the ever-changing influence and interconnectedness of global stock markets during similar political events.

The Benford law applied within complex networks is an interesting area of research. This paper proposes a new algorithm for the generation of a Benford network based on priority rank, and further specifies the formal definition. The condition to be taken into account is the probability density of the node degree. In addition to this first algorithm, an iterative algorithm is proposed based on rewiring. Its development requires the introduction of an ad hoc measure for understanding how far an arbitrary network is from a Benford network. The definition is a semi-distance and does not lead to a distance in mathematical terms, instead serving to identify the Benford network as a class. The semi-distance is a function of the network; it is computationally less expensive than the degree of conformity and serves to set a descent condition for the rewiring. The algorithm stops when it meets the condition that either the network is Benford or the maximum number of iterations is reached. The second condition is needed because only a limited set of densities allow for a Benford network. Another important topic is assortativity and the extremes which can be achieved by constraining the network topology; for this reason, we ran simulations on artificial networks and explored further theoretical settings as preliminary work on models of preferential attachment. Based on our extensive analysis, the first proposed algorithm remains the best one from a computational point of view.

In this work, we focus on the cross-shareholding structure in financial markets. Specifically, we build ad hoc indices of concentration and control by employing a complex network approach with a weighted adjacency matrix. To describe their left and right tail dependence properties, we explore the theoretical dependence structure between such indices through copula functions. The theoretical framework has been tested over a high-quality dataset based on the Italian Stock Market. In doing so, we clearly illustrate how the methodological setting works and derive financial insights. In particular, we advance calibration exercises on parametric copulas under the minimization of both Euclidean distance and entropy measure.

In this paper, we analyze the Italian pension funds and their declared benchmarks, which are market indexes. Within this perspective, the amounts invested in accord to the declared benchmarks can be analyzed like as a portfolio of benchmarks. We aim at understanding whether the pension funds investments are in line with the optimal portfolios which can be built through the declared benchmarks. To achieve the results, we set up a portfolio optimization problem building two networks of pension funds: one based on the (Pearson) correlation, and the other measuring the tail correlation. For each network, we use the local clustering coefficients to describe the level of connectivity, and we insert it in the risk function. This approach allows us to consider the network measures directly in the portfolio optimization model. We compare the results with the classical Markowitz setting, and we find a new efficient frontier overperforming the Markowitz one. A comparison among the performances of pension funds and their declared portfolio of benchmarks is also reported.

In this paper, techniques proper to complex networks studies have been applied to analyze features of the investment styles and similarities in the Italian pension funds. The analysis has been developed through interdisciplinary approaches. First, we look at the node degree distributions; next, we consider the centrality measures, like betweenness and closeness. Results indicate that the network of funds is dense and assortative, with short path lengths. Moreover, through community detection algorithms, it is found that many funds show similar features. In particular, the network of benchmarks is far from being dense, is characterized by hubs, and is disassortative. Furthermore, the insertion of weights does not produce dramatic changes in the centrality measures, but it blurs the communities. Still, the k-core and the highest k-shell do properly evidence the most popular benchmarks. In conclusion, the network structure of the Italian pension funds, without taking into account information from weights, seems to contain already sufficient information for detecting similarities in investments styles.

This paper answers the research question of the impact of extreme climate phenomena on bond returns. The question in answered by means of a factor model. Particularly, we add a climate factor to the classical bond market factors. The climate factor is constructed leveraging a novel methodology that permits the transposition of country-level climate related GDP losses into firm-level climate related fixed assets losses. The climatic factor proxies for the risk factor in bond returns related to extreme climate phenomena. The sensitivities of bond portfolios to the climatic factor are found to be statistically highly significant in most cases. We supplement the analysis with a climate stress test able to show the impact of plausible but more severe extreme climate phenomena on bond returns.

In this work, we develop the Tsallis entropy approach for examining the cross-shareholding network of companies traded on the Italian stock market. In such a network, the nodes represent the companies, and the links represent the ownership. Within this context, we introduce the out-degree of the nodes-which represents the diversification-and the in-degree of them-capturing the integration. Diversification and integration allow a clear description of the industrial structure that were formed by the considered companies. The stochastic dependence of diversification and integration is modeled through copulas. We argue that copulas are well suited for modelling the joint distribution. The analysis of the stochastic dependence between integration and diversification by means of the Tsallis entropy gives a crucial information on the reaction of the market structure to the external shocks-on the basis of some relevant cases of dependence between the considered variables. In this respect, the considered entropy framework provides insights on the relationship between in-degree and out-degree dependence structure and market polarisation or fairness. Moreover, the interpretation of the results in the light of the Tsallis entropy parameter gives relevant suggestions for policymakers who aim at shaping the industrial context for having high polarisation or fair joint distribution of diversification and integration. Furthermore, a discussion of possible parametrisations of the in-degree and out-degree marginal distribution-by means of power laws or exponential functions- is also carried out. An empirical experiment on a large dataset of Italian companies validates the theoretical framework.

This paper answers the research question of the impact of extreme climate events on stock returns. The article makes four contributions. Firstly, a method that permits the transposition of country-level climate related GDP losses into firm- level climate related fixed assets losses is put forward. Secondly, an economically significant factor that proxies for the risk factor in stock returns related to extreme climate events, LME, is proposed and tested in a Fama and French framework. Thirdly, the sensitivities of stock portfolios to the LME factor are found to be statistically highly significant. Fourthly, a climate stress test based upon the LME factor is presented. The climate stress test is able to show the impact of plausible but more severe extreme climate phenomena on stock returns.

This paper introduces a new temperature index, which can suitably represent the underlying of a weather derivative. Such an index is defined as the weighted mean of daily average temperatures measured in different locations. It may be used to hedge volumetric risk, that is the effect of unexpected fluctuations in the demand/supply for some specific commodities—of agricultural or energy type, for example—due to unfavorable temperature conditions. We aim at exploring the long term memory property of the volatility of such an index, in order to assess whether there exist some long-run paths and regularities in its riskiness. The theoretical part of the paper proceeds in a stepwise form: first, the daily average temperatures are modeled through autoregressive dynamics with seasonality in mean and volatility; second, the assessment of the distributional hypotheses on the parameters of the model is carried out for analyzing the long term memory property of the volatility of the index. The theoretical results suggest that the single terms of the index drive the long memory of the overall aggregation; moreover, interestingly, the proper selection of the parameters of the model might lead both to cases of persistence and antipersistence. The applied part of the paper provides some insights on the behaviour of the volatility of the proposed index, which is built starting from single daily average temperature time series.

This paper explores the issue of robustness against failure cascades for the network of interbank exposures. The available data were retrieved through the Bank for International Settlements database and report only incomplete information from which networks displaying a core-periphery structure were produced. A model of financial contagion was set up to estimate the width and length of the cascades, and was run on the networks detected from the data, as well as simulated data. The role of incomplete information was taken into account by considering a worst-case scenario in which unobserved links were assumed to be present. Given the core-periphery structure of the network, the worst-case scenario was studied in different sub-cases in which different periphery organisations were considered. Simulations showed that the actual network was far from the worst scenario for the propagation of contagion, meaning that the role of unobserved links can substantially alter the resilience of the whole network.

This paper deals with the analysis of the long-run behavior of a set of mispricing portfolios generated by three crude oils, where one of the oils is the reference commodity and it is compared to a combination of the other two ones. To this aim, the long-term parameter related to the mispricing portfolio are estimated on empirical data. We pay particular attention to the cases of mispricing portfolios either of stationary type or following a Brownian motion: the former situation is associated to replication portfolios of a reference commodity; the latter one allows to implement forecasts. The theoretical setting is validated through empirical data on WTI, Brent and Dubai oils.

The complex nature of the interlacement of economic actors is quite evident at the level of the Stock market, where any company may actually interact with the other companies buying and selling their shares. In this respect, the companies populating a Stock market, along with their connections, can be effectively modeled through a directed network, where the nodes represent the companies, and the links indicate the ownership. This paper deals with this theme and discusses the concentration of a market. A cross-shareholding matrix is considered, along with two key factors: the node out-degree distribution which represents the diversification of investments in terms of the number of involved companies, and the node in-degree distribution which reports the integration of a company due to the sales of its own shares to other companies. While diversification is widely explored in the literature, integration is most present in literature on contagions. This paper captures such quantities of interest in the two frameworks and studies the stochastic dependence of diversification and integration through a copula approach. We adopt entropies as measures for assessing the concentration in the market. The main question is to assess the dependence structure leading to a better description of the data or to market polarization (minimal entropy) or market fairness (maximal entropy). In so doing, we derive information on the way in which the in- and out-degrees should be connected in order to shape the market. The question is of interest to regulators bodies, as witnessed by specific alert threshold published on the US mergers guidelines for limiting the possibility of acquisitions and the prevalence of a single company on the market. Indeed, all countries and the EU have also rules or guidelines in order to limit concentrations, in a country or across borders, respectively. The calibration of copulas and model parameters on the basis of real data serves as an illustrative application of the theoretical proposal.

How much is the h-index of an editor of a well-ranked journal improved due to citations which occur after his/her appointment? Scientific recognition within academia is widely measured nowadays by the number of citations or h-index. Our dataset is based on a sample of four editors from a well-ranked journal (impact factor, IF, greater than 2). The target group consists of two editors who seem to benefit by their position through an increased citation number (and subsequently h-index) within the journal. The total amount of citations for the target group is greater than 600. The control group is formed by another set of two editors from the same journal whose relations between their positions and their citation records remain neutral. The total amount of citations for the control group is more than 1200. The timespan for which the citations’ pattern has been studied is 1975–2015. Previous coercive citations for a journal’s benefit (an increase of its IF) has been indicated. To the best of our knowledge, this is a pioneering work on coercive citations for personal (editors’) benefit. Editorial teams should be aware about this type of potentially unethical behavior and act accordingly.