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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.

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.

This article investigates the behaviour of the European banking system during the financial crises that occurred in the last decades. Among the various approaches for measuring systemic risk, we consider network analysis, which describes the linkages among financial institutions and their whole structure. We construct a time-varying network of the European banking system. Banks are linked to form a global interconnected system and they mutually influence one another in terms of risk. We model their reciprocal influence via a weighted and directed network, in which weights are related to risk measures that are based on equity returns. Then, we apply two network indicators to investigate the prominence of a bank in spreading and receiving risk from the others. The results enable us to capture many features of the banking system while identifying the global systemically important banks. Moreover, the results of the analysis over time show how interconnections change over periods that are characterized by various economic scenarios.

Different lexical resources may pursue different views on lexical meaning. However, all of them deal with lexical items as common basic components, which are described according to criteria that may vary from one resource to another. In this paper, we present a method for measuring the degree of similarity between a valency-based lexical resource and a WordNet. This is motivated by both theoretical and practical reasons. As for the former, we wonder if there are lexical classes that "impose" themselves regardless of the fact that they are explicitly recorded as such in source lexical resources. As for the latter, our work wants to contribute to the research task dealing with merging lexical resources. In order to apply and evaluate our method, we propose a normalized coefficient of overlapping that measures the overlapping rate between a valency lexicon and a WordNet. In particular, in the context of the exploitation of the linguistic resources for ancient languages built over the last decade, we compute and evaluate the overlapping between a selection of homogeneous lexical subsets extracted from two lexical resources for Latin.

Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node "importance" produced not only by the variation of the topology of the system but also as a consequence of the external levels of risk to which the network as a whole is submitted. Starting from the "Susceptible-Infected" (SI) model of epidemics and its relation to the communicability functions of networks we develop a series of risk-dependent centralities for nodes in (financial and economic) networks. We analyze here some of the most important mathematical properties of these risk-dependent centrality measures. In particular, we study the newly observed phenomenon of ranking interlacement, by means of which two entities may interlace their ranking positions in terms of risk in the network as a consequence of the change in the external conditions only, i.e., without any change in the topology. We test the risk-dependent centralities by studying two real-world systems: the network generated by collecting assets of the S\&P 100 and the corporate board network of the US top companies, according to Forbes in 1999. We found that a high position in the ranking of the analyzed financial companies according to their risk-dependent centrality corresponds to companies more sensitive to the external market variations during the periods of crisis., This version is accepted on SIAM journal on Financial Mathematics

This study shows that interconnections in the global banking network decreased due to the global financial crisis and subsequent regulatory initiatives. It also proves the effectiveness of the regulations of global systemically important banks in inducing these banks to contain their systemic nature.

New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line Non-Life insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naïve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out.

Solvency II Directive introduced a new framework in order to develop new risk management practices to manage risk and to define a minimum capital requirement. To this aim, Commission Delegated Regulation provided the final version of the standard formula. Capital requirement is obtained via a modular structure where each source of risk must be first measured and then aggregated under a linear correlation assumption. As the results of main Quantitative Impact Studies have shown, premium and reserve risks represent a key driver for non-life insurers. In this regard, we focus here on the valuation of the capital requirement for this specific sub-module. Some inconsistencies of the approach provided by Solvency II will be highlighted. We show that some assumptions of the standard formula may lead to an underestimation of the capital requirement for small insurers.

In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433–446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.

The future revision of capital requirements and a market-consistent valuation of non-hedgeable liabilities lead to an increasing attention on forecasting longevity trends. In this field, many methodologies focus on either modeling mortality or pricing mortality-linked securities (as longevity bonds). Following Lee–Carter method (proposed in 1992), actuarial literature has provided several extensions in order to consider different trends observed in European data set (e.g., the cohort effect). The purpose of the paper is to compare the features of main mortality models proposed over the years. Model selection became indeed a primary task with the aim to identify the “best” model. What is meant by best is controversial, but good selection techniques are usually based on a good balance between goodness of fit and simplicity. In this regard, different criteria, mainly based on residual and projected rates analysis, are here used. For the sake of comparison, main forecasting methods have been applied to deaths and exposures to risk of male Italian population. Weaknesses and strengths have been emphasized, by underlying how various models provide a different goodness of fit according to different data sets. At the same time, the quality and the variability of forecasted rates have been compared by evaluating the effect on annuity values. Results confirm that some models perform better than others, but no single model can be defined as the best method.

In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group. Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the i...