A simple mechanism leading to first-order phase transitions in a model of tax evasion

In this work, we study a dynamics of tax evasion. We considered a fully-connected population divided in three compartments, namely honest tax payers, tax evaders and susceptibles, a class that is composed by honest tax payers that can become evaders. We consider a contagion model where the transitions among the compartments are governed by probabilities. Such probabilities represent the possible interactions among the individuals, as well as the government fiscalization. We show by analytical and numerical calculations that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium first-order phase transition. In the absorbing phase, only honest tax payers survive in the steady states of the model, and we observe a coexistence of the three subpopulations in the active phase.

Systemic liquidity contagion in the European interbank market

Systemic liquidity risk, defined by the International Monetary Fund as “the risk of simultaneous liquidity difficulties at multiple financial institutions,” is a key topic in financial stability studies and macroprudential policy-making. In this context, the complex web of interconnections of the interbank market plays the crucial role of allowing funding liquidity shortages to propagate between financial institutions. Here, we introduce a simple yet effective model of the interbank market in which liquidity shortages propagate through an epidemic-like contagion mechanism on the network of interbank loans. The model is defined by using aggregate balance sheet information of European banks, and it exploits country and bank-specific risk features to account for the heterogeneity of financial institutions. Moreover, in order to obtain the European-wide topology of the interbank network, we define a block reconstruction method based on the exchange flows between the various countries. We show that the proposed contagion model is able to estimate systemic liquidity risk across different years and countries. Results suggest that our effective contagion approach can be successfully used as a viable alternative to more realistic but complicated models, which not only require more specific balance sheet variables with high time resolution but also need assumptions on how banks respond to liquidity shocks.

A Dynamic Contagion Risk Model with Recovery Features

We introduce threshold growth in the classical threshold contagion model, or equivalently a network of Cramér-Lundberg processes in which nodes have downward jumps when there is a failure of a neighboring node. Choosing the configuration model as underlying graph, we prove fluid limits for the baseline model, as well as extensions to the directed case, state-dependent interarrival times and the case of growth driven by upward jumps. We obtain explicit ruin probabilities for the nodes according to their characteristics: initial threshold and in- (and out-) degree. We then allow nodes to choose their connectivity by trading off link benefits and contagion risk. We define a rational equilibrium concept in which nodes choose their connectivity according to an expected failure probability of any given link and then impose condition that the expected failure probability coincides with the actual failure probability under the optimal connectivity. We show existence of an asymptotic equilibrium and convergence of the sequence of equilibria on the finite networks. In particular, our results show that systems with higher overall growth may have higher failure probability in equilibrium.

Planned Obsolescence with Network Effects

This paper appeals to the interplay between network effects and quality to justify the use of planned obsolescence by well-settled firms. We propose a simple contagion model to analyze an asymmetric duopoly market where an incumbent firm benefits, at least initially, from the first‐mover advantages attributed to network industries, while the entrant offers a product with higher quality. The simpler version of the model describes the evolution of the market shares, showing that network effects can overtake the quality effect if the market is sufficiently small. If the market lasts enough, network effects end up enhancing the effect of quality and the entrant gets a higher market share. If the incumbent can set the size of the market by launching a new product every so often, the model provides a rationale for the use of planned obsolescence from a strategic point of view. Social efficiency is then challenged.

State-based targeted vaccination

Vaccination has become one of the most prominent measures for preventing the spread of infectious diseases in modern times. However, mass vaccination of the population may not always be possible due to high costs, severe side effects, or shortage. Therefore, identifying individuals with a high potential of spreading the disease and targeted vaccination of these individuals is of high importance. While various strategies for identifying such individuals have been proposed in the network epidemiology literature, the vast majority of them rely solely on the network topology. In contrast, in this paper, we propose a novel targeted vaccination strategy that considers both the static network topology and the dynamic states of the network nodes over time. This allows our strategy to find the individuals with the highest potential to spread the disease at any given point in time. Extensive evaluation that we conducted over various real-world network topologies, network sizes, vaccination budgets, and parameters of the contagion model, demonstrates that the proposed strategy considerably outperforms existing state-of-the-art targeted vaccination strategies in reducing the spread of the disease. In particular, the proposed vaccination strategy further reduces the number of infected nodes by 23–99%, compared to a vaccination strategy based on Betweenness Centrality.

Pandemic risk: operational aspects

At the beginning of the COVID-19 pandemic, Intesa Sanpaolo has developed a contagion model aimed at calibrating the measures to be taken to safeguard its employees and the provision of banking services, according to the risk deriving from the external environment. The model is based on both external and internal views: the combination of such elements provides a holistic picture of the overall contagion risk level, enabling the opportunity to take informed decisions for each geographical area. One of the most useful external indicators to feed the model is the reproduction index (Rt) provided by the University of Pavia which is calculated using the Poisson autoregressive (PAR) model. Though more research and development are needed, the proposed model represents a useful tool for supporting the Top Managers in the decision process to continue business as usual safely.