Systemic risk assessment through high order clustering coefficient

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.Comment: Submitte

Bounding robustness in complex networks under topological changes through majorization techniques

Measuring robustness is a fundamental task for analyzing 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 realworld 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 (Schurconvex functions). Applications to simulated graphs show the effectiveness of our bounds, also in providing meaningful insights with respect to the results obtained in the literature

Taxonomy of Cohesion Coefficients for Weighted and Directed Multilayer Networks

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

Community structure in the World Trade Network based on communicability distances

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.Comment: 40 pages, 19 figure

Multi-criteria community detection in International Trade Network

Understanding the community structure has great importance for economic analysis. Communities are characterized by properties different from those of both the individual node and the whole network and they affect various processes on the network. We combine community detection with specific topological indicators. As a result, a new weighted network is constructed by the original one, in which weights are determined taking into account all the topological indicators in a multi-criteria approach. We introduce a new algorithm to detect communities by solving the NP-hard CP-problem

The Effect of Non-Proportional Reinsurance: A Revision of Solvency II Standard Formula

Solvency II Standard Formula provides a methodology to recognise the risk-mitigating impact of excess of loss reinsurance treaties in premium risk modelling. We analyse the proposals of both Quantitative Impact Study 5 and Commission Delegated Regulation highlighting some inconsistencies. This paper tries to bridge main pitfalls of both versions. To this aim, we propose a revision of non-proportional adjustment factor in order to measure the effect of excess of loss treaties on premium risk volatility. In this way, capital requirement can be easily assessed. As numerical results show, this proposal appears to be a feasible and much more consistent approach to describe the effect of non-proportional reinsurance on premium ris

A cohort-based Partial Internal Model for demographic risk

We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance policies based on a cohort approach. In this context, we maintain the highest level of generality in order to consider both traditional policies and equity-linked policies: therefore, we propose a market-consistent valuation of the liabilities. In the second step we evaluate the Solvency Capital Requirement of the idiosyncratic risk, linked to accidental mortality, and the systematic risk one, also known as trend risk, proposing a formal closed formula for the former and an algorithm for the latter. We show that accidental volatility depends on the intrinsic characteristics of the policies of the cohort (Sums-at-Risk), on the age of the policyholders and on the variability of the sums insured; trend risk depends both on accidental volatility and on the longevity forecasting model used