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This paper provides a stochastic model, consistent with Solvency II and the Delegated Regulation, to quantify the capital requirement for demographic risk. In particular, we present a framework that models idiosyncratic and trend risks exploiting a risk theory approach in which results are obtained analytically. We apply the model to non-participating policies and quantify the Solvency Capital Requirement for the aforementioned risks in different time horizons.

In the complex global food system, the dynamics associated to international food trade became key determinants of foodsecurity. In this paper, we combine a community detection approach with a supervised learning technique in order to describeboth the evolution and the resilience of agri-food trade network. Using a large amount of data, we detect similarities betweencountries and we identify the main drivers that affect trade dynamics over time. The analysis is completed also including thevariability on food production and trading due to the climate conditions’ evolution. Results emphasize how the topologicalstructure of the network is evolving over time and how it is modifying the clusters composition. Interestingly, we identifysustainability, climate and food nutrition aspects between the emerging factors in the explanation of trade relationships.

In this paper, we provide novel definitions of clustering coefficient for weighted and directed multilayer networks. We extend in the multilayer theoretical context the clustering coefficients proposed in the literature for weighted directed monoplex networks. We quantify how deeply a node is involved in a cohesive structure focusing on a single node, a single layer or the entire system, respectively. The coefficients convey several characteristics inherent to the complex topology of the multilayer network. We test their effectiveness applying them to a particularly complex structure such as the international trade network. The trade data integrate different aspects and they can be described by a directed and weighted multilayer network, where each layer represents import and export relationships between countries for a given sector. The proposed coefficients find successful application in describing the interrelations of the trade network, allowing to disentangle the effects of countries and sectors and jointly consider the interactions between them.

This paper proposes an optimal allocation model with the main aim to minimize systemic risk related to the sovereign risk of a set of countries. The reference methodological environment is that of complex networks theory. Specifically, we consider the weighted clustering coefficient as a proxy of systemic risk, while the interconnections among countries are captured by the relationships among default probabilities of the set of countries under consideration. The selected optimization criterion is based on minimization of the mean absolute deviation. We perform empirical analyses to validate the theoretical predictions, and interpret the findings in the context of the proposed model.

In this paper, we provide a methodology suitable to identify relevant insurance companies in a systemic risk framework. To this end, we propose a complex network approach where insurers are linked to form a global interconnected system. In particular, we extend the current literature proposing an approach based on a directed weighted multilayer network. The reciprocal influence between insurers is indeed considered in each period and in subsequent periods, calibrating arc weights on the basis of specific risk measures. Hub and authority scores are then used to assess the prominence of a company in spreading and receiving risk from the others.

Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted networks, where the choice of the weight attributed to the triangles is a crucial aspect. In the present work, in the framework of weighted directed multilayer networks, we extend the classical clustering and closure coefficients through the introduction of the clumping coefficient, which generalizes them to incomplete triangles of any type. We then organize the class of these coefficients in a systematic taxonomy in the more general context of weighted directed multilayer networks. Such cohesion coefficients have also been adapted to the different scales that characterize a multilayer network, in order to grasp their structure from different perspectives. We also show how the tensor formalism allows incorporating the new definitions, as well as all those existing in the literature, in a single unified writing, in such a way that a suitable choice of the involved adjacency tensors allows obtaining each of them. Finally, through some applications to simulated networks, we show the effectiveness of the proposed coefficients in capturing different peculiarities of the network structure on different scales.

In this work, we propose a novel robustness measure for networks, which we refer to as Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the Kirchhoff index due to deletion of this vertex (edge) from the network. Indeed, we provide a local robustness measure, able to catch which is the effect of either a specific vertex or a specific edge on the network robustness. The validness of this new measure is illustrated on some typical graphs and on a wide variety of well-known model networks. Furthermore, we analyse the topology of the US domestic flight connections. In particular, we investigate the role that airports play in maintaining the structure of the entire network.

The main contribution of the paper is to employ the financial market network as a useful tool to improve the portfolio selection process, where nodes indicate securities and edges capture the dependence structure of the system. Three different methods are proposed in order to extract the dependence structure between assets in a network context. Starting from this modified structure, we formulate and then we solve the asset allocation problem. We find that the portfolios obtained through a network-based approach are composed mainly of peripheral assets, which are poorly connected with the others. These portfolios, in the majority of cases, are characterized by an higher trade-off between performance and risk with respect to the traditional Global Minimum Variance (GMV) portfolio. Additionally, this methodology benefits of a graphical visualization of the selected portfolio directly over the graphic layout of the network, which helps in improving our understanding of the optimal strategy., Submitted

Big data and the use of advanced technologies are relevant topics in the financial market. In this context, complex networks became extremely useful in describing the structure of complex financial systems. In particular, the time evolution property of the stock markets have been described by temporal networks. However, these approaches fail to consider the interactions over time between assets. To overcome this drawback, financial markets can be described by multiplex networks where the different relations between nodes can be conveniently expressed structuring the network through different layers. To catch this kind of interconnections we provide new local clustering coefficients for multiplex networks, looking at the network from different perspectives depending on the node position, as well as a global clustering coefficient for the whole network. We also prove that all the well-known expressions for clustering coefficients existing in the literature, suitably extended to the multiplex framework, may be unified into our proposal. By means of an application to the multiplex temporal financial network, based on the returns of the S\&P100 assets, we show that the proposed measures prove to be effective in describing dependencies between assets over time.

Understanding the structure of communities in a network has a great importance in the economic analysis. Communities are indeed characterized by specific properties, that are different from those of both the individual nodes and the whole network, and they can affect various processes on the network. In the International Trade Network, community detection aims to search sets of countries (or of trade sectors) which have a high intra-cluster connectivity and a low inter-cluster connectivity. In general, exchanges among countries occur according to preferential economic relationships ranging over different sectors. In this paper, we combine community detection with specific topological indicators, such as centrality measures. As a result, a new weighted network is constructed from the original one, in which weights are determined taking into account all the topological indicators in a multi-criteria approach. To solve the resulting Clique Partitioning Problem and find homogeneous group of nations, we use a new fast algorithm, based on quick descents to a local optimal solution. The analysis allows to cluster countries by interconnections, economic power and intensity of trade, giving an important overview on the international trade patterns.

We analyse the multilayer architecture of the global input-output network using sectoral trade data (WIOD, 2016 release). With a focus on the mesoscale structure and related properties, we find that the multilayer analysis that takes into consideration the splitting into industry-based layers is able to catch more peculiar relationships between countries that cannot be detected from the analysis of the single-layer aggregated network. We can identify several large international communities in which some countries trade more intensively in some specific layers. However, interestingly, our results show that these clusters can restructure and evolve over time. In general, not only their internal composition changes, but the centrality rankings of the members inside are also reordered, with the diminishing role of industries from some countries and the growing importance of those from some other countries. These changes in the large international clusters may reflect the outcomes and the dynamics of cooperation as well as competition among industries and among countries in the global input-output network.

Measuring robustness is a fundamental task for analysing the structure of complex networks. Indeed, several approaches to capture the robustness properties of a network have been proposed. In this paper we focus on spectral graph theory where robustness is measured by means of a graph invariant called Kirchhoff index, expressed in terms of eigenvalues of the Laplacian matrix associated to a graph. This graph metric is highly informative as a robustness indicator for several real-world networks that can be modeled as graphs. We discuss a methodology aimed at obtaining some new and tighter bounds of this graph invariant when links are added or removed. We take advantage of real analysis techniques, based on majorization theory and optimization of functions which preserve the majorization order. Applications to simulated graphs and to empirical networks generated by collecting assets of the S&P 100 show the effectiveness of our bounds, also in providing meaningful insights with respect to the results obtained in the literature. Graphical abstract: [Figure not available: see fulltext.].

The increasing role of technology is generating new challenges in fostering innovative insurance products and in offering new means of distribution for existing products. Herein, we focus on peer-to-peer insurance, where technology is used to connect policyholders and the insurance structure recalls its roots based on organised mutual solidarity. The aim is to highlight strengths and weaknesses of the broker model of peer-to-peer insurance. We address the main legal and regulatory issues by referring to European Union regulation on insurance and we develop an actuarial model to support our conclusions and evaluate the convenience of such a business model for policyholders. Although peer-to-peer insurance was created as a fairer alternative to the pool of traditional insurance companies, we see major challenges that need to be solved. The evidence sheds doubt on the convenience of the broker model for peer-to-peer insurance while the regulatory risks seem, paradoxically, certain.

In this article we propose a novel measure of systemic risk in the context of financial networks. To this aim, we provide a definition of systemic risk which is based on the structure, developed at different levels, of clustered neighbours around the nodes of the network. The proposed measure incorporates the generalized concept of clustering coefficient of order $l$ of a node $i$ introduced in Cerqueti et al. (2018). Its properties are also explored in terms of systemic risk assessment. Empirical experiments on the time-varying global banking network show the effectiveness of the presented systemic risk measure and provide insights on how systemic risk has changed over the last years, also in the light of the recent financial crisis and the subsequent more stringent regulation for globally systemically important banks., Submitted

In this paper, we investigate the mesoscale structure of the World Trade Network. In this framework, a specific role is assumed by short and long-range interactions, and hence by the distance, between countries. Therefore, we identify clusters through a new procedure that exploits Estrada communicability distance and the vibrational communicability distance, which turn out to be particularly suitable for catching the inner structure of the economic network. The proposed methodology aims at finding the distance threshold that maximizes a specific modularity function defined for general metric spaces. Main advantages regard the computational efficiency of the procedure as well as the possibility to inspect intercluster and intracluster properties of the resulting communities. The numerical analysis highlights peculiar relationships between countries and provides a rich set of information that can hardly be achieved within alternative clustering approaches., 40 pages, 19 figures