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Modern energy systems are increasingly vital for the delivery of various essential services. These services include clean water, sanitation, healthcare, reliable and efficient lighting, heating, cooking, mechanical power, transportation, and telecommunications. The adoption of modern energy systems has resulted in notable enhancements in the quality of life for a significant portion of the global population. Typically, an energy system encompasses a complex and comprehensive structure that considers various elements such as energy production, transformation, transport, and distribution. In recent times, a great importance has been devoted to energy security, which is essential for the well-being associated with energy. Energy security involves two main aspects: longterm investments to align energy supply with economic and environmental needs, and short-term focus on the energy system’s ability to respond swiftly to supply-demand shifts and maintain resilience. Furthermore, it is crucial to establish a strong connection between energy security and climate change mitigation initiatives. Indeed, as highlighted in [9], in order to maximize the effectiveness of their energy policy, nations must integrate considerations of energy security and climate change mitigation priorities concurrently. Countries should prioritize both to optimize their energy policies’ efficiency, as referenced in . Energy access also presents a significant issue of inequality, with uneven distribution of energy sources across the globe. This lack of equitable access to energy sources poses challenges for sustainable development (see [13], [14] and [7]). Several factors drive the evaluation of energy system resilience and guide policymakers towards sustainable policies. These include energy consumption, the transfer of direct and indirect energy resources through international trade, transitioning to renewable energies, and promoting environmental sustainability. In this context, it is common pract

We propose a flexible link forecast methodology for weighted temporal networks. Our probabilistic model estimates the evolving link dynamics among a set of nodes through Wasserstein barycentric coordinates arising within the optimal transport theory. Optimal transport theory is employed to interpolate among network evolution sequences and to compute the probability distribution of forthcoming links. Besides generating point link forecasts for weighted networks, the methodology provides the probability that a link attains weights in a certain interval, namely a quantile of the weights distribution. We test our approach to forecast the link dynamics of the worldwide Foreign Direct Investments network and of the World Trade Network, comparing the performance of the proposed methodology against several alternative models. The performance is evaluated by applying non-parametric diagnostics derived from binary classifications and error measures for regression models. We find that the optimal transport framework outperforms all the competing models when considering quantile forecast. On the other hand, for point forecast, our methodology produces accurate results that are comparable with the best performing alternative model. Results also highlight the role played by model constraints in the determination of future links emphasising that weights are better predicted when accounting for geographical rather than economic distance.

We propose a new paradigm to design a network-based self-adaptive epidemic model that relies on the interplay between the network and its line graph. We implement this proposal on a susceptible-infected-susceptible model in which both nodes and edges are considered susceptible and their respective probabilities of being infected result in a real-time re-modulation of the weights of both the graph and its line graph. The new model can be considered as an appropriate perturbation of the standard susceptible-infected-susceptible model, and the coupling between the graph and its line graph is interpreted as a reinforcement factor that fosters diffusion through a continuous adjustment of the parameters involved. We study the existence and stability conditions of the endemic and disease-free states for general network topologies. Moreover, we introduce, through the asymptotic values in the endemic steady states, a new type of eigenvector centrality where the score of a node depends on both the neighboring nodes and the edges connected to it. We also investigate the properties of this new model on some specific synthetic graphs, such as cycle, regular, and star graphs. Finally, we perform a series of numerical simulations and prove their effectiveness in capturing some empirical evidence on behavioral adoption mechanisms.

Climate change represents a relatively new risk compared with other traditional insurance and financial risks. Nevertheless, it gained priority in the agendas of governments, public institutions, and private stakeholders. Climate change mainly involves two kinds of risks: the physical and the transitional risks. The former determines effects directly from climate change due to the physical impact of increasing severity and frequency of extreme climate change-related weather events, and the latter effects arising from the change to a carbon-neutral economy, to meet the objectives of the Paris Climate Agreement. The main features of climate-related risks rely on the long-term nature of the related events, being the impact likely structural, irreversible, and non-linear (European Insurance and Occupational Pensions Authority [EIOPA], 2022). They affect the insurability of risks, impacting on affordability and availability of financial and insurance products, also determining the protection gap. Typically protection gaps are areas in which societal risks are not covered by the insurance industry, either because of lack of penetration, or because the risks are uninsurable in profit-oriented markets. In this chapter, we support the early identification of protection gaps and the development of shared resilience solutions between the insurance industry and public protection facilities, by setting out methodological toolboxes in the agribusiness context. Agriculture both contributes to climate change and is affected by climate change. Crops need suitable soil, water, sunlight, and heat to grow. Warmer air temperatures have already affected the length of the growing season over large parts of Europe. Flowering and harvest dates for cereal crops are now happening several days earlier in the season. These changes are expected to continue in many regions. In general, agriculture and forestry are highly exposed to the impact of rising global temperatures: increased fluctuations

I study the exact percentage price reaction (in absolute value) to changes in the short rate for long-lived assets in a tractable long-run risk equilibrium model with fluctuating expected growth rates. Calibration reveals that, under time-additive expected utility, perpetuities with constant coupons exhibit a larger effective duration than the absolute value of the stock price logarithmic derivative due to a mild positive comovement between short rates and expected dividend growth. Conversely, under Epstein-Zin preferences with unit elasticity of intertemporal substitution, the perpetuity’s effective duration is smaller due to a pronounced positive comovement between short rates and expected dividend growth. My findings suggest that strong persistence in fundamentals contributes to non-linearities in the equilibrium log prices of long-lived assets. (JEL Classification Code: G12). Keywords: equilibrium short rate, long-run risk, effective duration, stock pricing, perpetuity/consol pricing.

According to the Solvency II directive, insurers can use internal models for solvency assessment, but regulators must approve these models. Sensitivity analysis is a crucial part of the approval process. However, the directive lacks clarity on the required sensitivity analysis. Various techniques exist in literature to assess the impact of model assumptions on output, each revealing different aspects of model behaviour. In this letter, we suggest a minimum standard for regulators to ensure model quality. We propose complementary sensitivity settings for internal model development, governance, and approval. Implementing these settings enhances the explainability of approved models and their reliability.

We provide, in every infinite -dimensional separable Banach space, an average locally uniformly rotund (and hence rotund) Gateaux smooth renorming which is not locally uniformly rotund. This solves an open problem posed in a recent monograph by A.J. Guirao, V. Montesinos, and V. Zizler.

This study addresses the assessment of capital requirements in life insurance for idiosyncratic demographic risks arising from mortality and longevity in compliance with the Solvency II framework. A closed-formula methodology, using a cohort-based risk theoretical approach, is introduced to properly capture the volatility associated with policyholder deaths or survivals. This approach not only accounts for portfolio size effects but it also considers the impact of variability in sums insured within cohorts and coverage types with an additional specific address to distribution tails. The proposed methodology offers a viable alternative within the Solvency II context, addressing limitations identified in previous studies for the Standard Formula nowadays in force. Focusing only on the diversifiable part of demographic risk, the approach considers company’s specific parameters through a risk-based formula, as opposed to a simple scenario approach with demographic stress on the Best Estimate of underlying contracts valid for the whole business. Numerical results show its accuracy in approximating capital requirements for a large range of life insurance contracts

This paper addresses the critical issue of road safety and accident prevention by integrating road features, network theory, and advanced statistical models. It emphasises the importance of understanding the relationship between road infrastructure and accident risk, which impacts on various administrative stakeholders and on citizens’ safety. While existing literature focuses on road features and engineering solutions, this paper highlights the need to consider implicit spatial constraints as well. Our study builds on prior research by proposing a novel approach that merges conditional autoregressive modelling with a two-stage mixed Geographically weighted Poisson regression. This integrated methodology allows us to consider both the effect of risk factors at a global level and at a local road level. By leveraging the strengths of these two methods, we aim to capture both overarching trends and local variations of risk factors, thereby offering a comprehensive understanding of accident risk factors. Using data from the Open Street Map database, which covers the wide province of Milan in Italy, our models identify influential street characteristics, providing valuable insights for informed decision-making regarding road safety measures. Our method can be applied to any region in the world. The paper describes the models used, the dataset employed, and presents a detailed numerical analysis demonstrating the effectiveness of the approach in identifying and understanding accident risk factors within road networks. This information can help guide investments for the benefit of society.

We construct a model where, at each time instance, risky securities can only take a limited number of values and the equity-linked policy sold by the insurer to policyholders pays benefits linked to these securities. Since the number of states in the model exceeds the number of securities in the (incomplete) market, the martingale measure is not unique, posing a problem in pricing insurance instruments. In this framework, we consider how a super-replicating strategy violates the assumption of absence of arbitrage, yet simultaneously allows the insurance company to fully hedge against financial risk. Since the super-replicating strategy, when considered alone, would be too costly for any rational insured, through the definition of the safety loading, we demonstrate how the insurer can still hedge against financial risk, albeit at the expense of increasing its exposure to demographic risk. This approach does not aim to show how the pricing of the index-linked policy can actually be performed, but rather highlights how risk theory-based approaches (via the definition of the profit and loss random variable) enable the management of the trade-off between financial risk and demographic risk.

Over the last decade, insurance market has been characterized by significant changes. New regulations, as Solvency II (European Commission 2009) and IFRS17 (European Commission 2021) paved the way to an increasing focus on risk assessment and on market consistent valuation of assets and liabilities. Also the growth of artificial intelligence (AI), used to perform complex computational tasks, is revolutionising financial services, particularly within insurance practices (see EIOPA 2021). Nowadays, data represent a primary strategic asset and a source of competitive advantage in financial firms and the inherent value of predictive analytics in insurance is showing itself in myriad applications (see, e.g., Hyong and Errol 2015; Maynard et al. 2022). Additionally, an emerging wave of insurtech solutions are trying to transform insurance business through the introduction of Big Data, Machine Learning, and AI capabilities (see, e.g., McFall et al. 2020). In the insurance context, several fields have been characterized by the use of Machine Learning and AI methodologies. Predictive analytics tools can collect data from a variety of sources to better understand and predict the behaviour of policyholders. Companies are indeed collecting data from telematics, distribution channel and customers interactions, smart homes and even social media to better understand and manage their relationships, claims, and underwriting and so on.

La pubblicazione nasce per indicare agli studenti delle scuole superiori che intendono iscriversi alla Facoltà di Economia dell'Università Cattolica, e che devono quindi sostenere il test di ingresso, quali siano le conoscenze matematiche che verranno richieste nella parte del test ad esse dedicata; dall’altro, essere di supporto alle matricole che, pur avendo superato complessivamente il test di ingresso, non hanno ottenuto un punteggio sufficiente nella parte di matematica e hanno quindi l’obbligo dei debiti formativi aggiuntivi (OFA). La pubblicazione può essere utile anche a tutti gli studenti che, pur non avendo debiti formativi, desiderano consolidare la loro preparazione di base. La sua specificità risiede proprio nel fatto che è stata pensata e realizzata tenendo presente le esigenze della Facoltà di Economia dell'Università Cattolica, sebbene possa in linea di principio essere utile anche in altri contesti universitari.

The challenges of using technology in the insurance field are opening new horizons for developing and distributing innovative products. Among these, peer-to-peer insurance schemes attract the interest of policyholders and insurance companies. Different types of peer-to-peer insurance have been introduced, from pure models to hybrid ones, as in the case of the broker model. In this paper, we focus on the broker model, where the groups of peers are formed by an insurance broker according to similar risk characteristics. The participants in the network pay an initial contribution defined by a cooperative rule that must be transparent and shared. A part or the whole of the collected contributions is set aside in a common fund. At the end of the year, if the common fund is sufficient to pay for the claims, the members obtain the excess over-retained premiums that is shared according to a capital allocation rule. We propose a cashback distribution mechanism based on the participant’s marginal contribution to the risk, framing the issue in a cooperative game and applying the concept of Shapley value to define an optimal allocation rule of the remaining capital. A numerical application based on a portfolio of motor third-party liability policies is developed to show how the model works

In the last decade, the index-based weather products (also called weather derivatives) have been gaining attention in the climate resilience discussion. Weather derivatives are designed to help companies hedging against climate variability. These products, that can be market traded or over-the-counter, compensate individuals based on a pre-defined weather index. Thus, pay-offs of a weather derivative depend on a weather index and not, as with traditional types of insurance, on the actual amount of money lost due to adverse weather. One of the major drawbacks that may prevent weather derivatives to catch on is the impact of the Geographical Basis Risk (GBR), that is the deviation of weather conditions at different locations. In fact, when the reference weather station is not located in the immediate vicinity of the site of interest the hedging effectiveness may be reduced. In this paper, we contribute to the existing literature on GBR by proposing an optimization method that may help in offering a tailored solution, while at the same time keeping a standardized instrument as a reference. Using a historical record of Italian temperatures, strikes for temperatures are the choice variables of a penalty function containing pay-offs of a reference station and all other stations. Further, altitude and latitude of meteorological stations are shown to be relevant predictors to explain GBR. This can be an interesting starting point for the design of weather derivatives, since, from a unique station where the “reference” derivative is priced, all the other stations may be easily settled.

Il testo è la naturale prosecuzione dei testi “Note di Matematica: nozioni preliminari” e “Note di Matematica: esercizi”: gli argomenti contenuti in quei testi sono prerequisiti essenziali per poter comprendere le risoluzioni degli esercizi svolti di questo manuale e per poter affrontare autonomamente gli esercizi proposti. Il testo è composto da capitoli (associati agli argomenti principali trattati nel testo) suddivisi in 3 sezioni: la prima, di esercizi svolti, dove viene fornita allo studente una panoramica delle tipologie di esercizi e di tecniche risolutive; la seconda, dove vengono proposti esercizi da risolvere (con soluzioni) così che lo studente possa esercitarsi attivamente ed autonomamente sull’argomento; la terza, dove vengono proposti esercizi completamente svolti tratti da temi d’esame dei corsi di Matema- tica Generale II dell’Università Bicocca e di Matematica Generale dell’Università Cattolica, dall’A.A. 2002/03 ad oggi.

In this paper, we contribute to the topic of the non-performing loans (NPLs) business profitability on the secondary market by developing machine learning-based due diligence. In particular, a loan became non-performing when the borrower is unlikely to pay, and we use the ability of the ML algorithms to model complex relationships between predictors and outcome variables, we set up an ad hoc dependent random forest regressor algorithm for projecting the recovery rate of a portfolio of the secured NPLs. Indeed the profitability of the transactions under consideration depends on forecast models of the amount of net repayments expected from receivables and related collection times. Finally, the evaluation approach we provide helps to reduce the ”lemon discount” by pricing the risky component of informational asymmetry between better-informed banks and potential investors in particular for higher quality, collateralised NPLs.

In the complex global food system, the dynamics associated with international food trade have become crucial determinants of food security. In this paper, we employ a community detection approach along with a supervised learning technique to explore the evolution of communities in the agri-food trade network and to identify key factors influencing their composition. By leveraging a large dataset that includes both volume and monetary value of trades, we identify similarities between countries and uncover the primary drivers that shape trade dynamics over time. The analysis also takes into account the impact of evolving climate conditions on food production and trading. The results highlight how the network’s topological structure is continuously evolving, influencing the composition of communities over time. Alongside geographical proximity and geo-political relations, our analysis identifies sustainability, climate and food nutrition aspects as emerging factors that contribute to explaining trade relationships. These findings shed light on the intricate interactions within the global food trade system and provide valuable insights into the factors affecting its stability.

The energy consumption, the transfer of resources through the international trade, the transition towards renewable energies and the environmental sustainability appear as key drivers in order to evaluate the resilience of the energy systems. Concerning the consumptions, in the literature a great attention has been paid to direct energy, but the production of goods and services also involves indirect energy. Hence, in this work we consider different types of embodied energy sources and the time evolution of the sectors’ and countries’ interactions. Flows are indeed used to construct a directed and weighted temporal multilayer network based respectively on renewable and non-renewable sources, where sectors are nodes and layers are countries. We provide a methodological approach for analysing the network reliability and resilience and for identifying critical sectors and economies in the system by applying the Multi-Dimensional HITS algorithm. Then, we evaluate central arcs in the network at each time period by proposing a novel topological indicator based on the maximum flow problem. In this way, we provide a full view of economies, sectors and connections that play a relevant role over time in the network and whose removal could heavily affect the stability of the system.We provide a numerical analysis based on the embodied energy flows among countries and sectors in the period from 1990 to 2016. Results prove that the methods are effective in catching the different patterns between renewable and non-renewable energy sources.

We propose an elementary macroeconomic model with animal spirits in which aggregate investment expenditure depends on firms’ sentiment. Firms display one of three sentiment states. When national income increases (decreases) strongly, firms are optimistic (pessimistic) and aggregate investment expenditure is high (low). Otherwise, firms are neutral and aggregate investment expenditure is normal. A rigorous mathematical analysis of our elementary macroeconomic model sheds new light on how animal spirits may contribute to fluctuations in economic activity. In particular, we show that a bidirectional feedback process between national income and investor sentiment may create endogenous business cycles that coevolve with waves of optimism and pessimism.

Let $A$ be an open convex subset of a real normed linear space $X$. We prove that if the boundary of $A$ contains a non-LUR point then there exists a Lipschitz quasiconvex function $f\colon A\to \R$ not admitting any continuous quasiconvex extension to the whole $X$.

Starting from the work of Hommes et al. (2005a), we propose an alternative version of their asset pricing model with heterogeneous agents and asynchronous updating of beliefs. In particular, we assume that the predictors are selected based on their accuracy in predicting the market price of the risky asset, measured as an absolute prediction error, and not on the net profits made by fundamentalists and trend followers. From a mathematical point of view, the deterministic skeleton of the present model is a two-dimensional piecewise-smooth map. We present an analytical study of the fundamental equilibrium and the coexisting non-fundamental equilibria and propose a comparison with the results in Hommes et al. (2005a). A robustness check is also conducted by considering an accuracy measured by squared prediction errors, a fitness measure often adopted in theoretical and experimental studies because of its smoothness and for being equivalent to risk-adjusted profits. The comparisons reveal that these different fitness measures do not modify the stability of the fundamental equilibrium. However, non-fundamental equilibria, their stability and the out-of-equilibrium dynamics are affected.

The aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a generalization of both of them in set optimization with finite dimensional spaces, by considering also a special class of polyhedral ordering cone. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering convexity hypotheses.

This paper summarizes Gerd Weinrich's contribution to economics. His contribution to economics has a wide range and it includes: foundational concepts about non-Walrasian equilibria with stochastic rationing; original models of non-walrasian macroeconomics; contributions to monetary economics, economic growth and regulation of banks; studies of financial decisions under risk aversion, firms' behavior, asymmetric information and externalities.

A representation theorem proven by G. Debreu in 1960, although somehow neglected by the literature, implies several deep and unexplored consequences both for Economics and for Decision Theory. This paper focuses on some of them. In particular, possible decompositions of state-dependent utilities à la Debreu (which may equivalently be seen as ‘utility-dependent probabilities’) are analysed, showing that Debreu’s representation is based upon a ‘joint’ probability/utility function. It is illustrated how Debreu’s Theorem can provide a neat geometrical interpretation of Castagnoli and LiCalzi’s ‘benchmarking’ representation of preferences. (Conditional) Certainty Equivalents are defined and studied, and possible implications for attempting representation of incomplete preferences are discussed.

Let Y be a subspace of a topological vector space X, and A subset of X an open convex set that intersects Y. We say that the property (QE) [property (CE)] holds if every continuous quasiconvex [continuous convex] function on A il Y admits a continuous quasiconvex [continuous convex] extension defined on A. We study relations between (QE) and (CE) properties, proving that (QE) always implies (CE) and that, under suitable hypotheses (satisfied for example if X is a normed space and Y is a closed subspace of X), the two properties are equivalent. By combining the previous implications between (QE) and (CE) properties with known results about the property (CE), we obtain some new positive results about the extension of quasiconvex continuous functions. In particular, we generalize the results contained in [9] to the infinite-dimensional separable case. Moreover, we also immediately obtain existence of examples in which (QE) does not hold. (c) 2023 Elsevier Inc. All rights reserved.

Within the insurance field, the digital revolution has enabled the collection and storage of large quantities of information. This era is referred to as “big data”, since the great uncertainty to be modelled is too complex for traditional data processing techniques. For insurance purposes, big data refers to unstructured and/or structured data being used to influence underwriting, rating, pricing, forms, marketing and claims handling. The use of artificial intelligence (AI) in actuarial science is a rapidly growing area that is significantly impacting the insurance industry. This integration of technology involves both machine learning (ML) algorithms and data analysis to help actuaries develop more accurate risk assessments and predictions. With a larger possibility of accessing huge sets of data, actuaries can leverage AI to automate underwriting and claims processing, improve customer experience and provide valuable insights to insurers to perfect decision-making strategies. In this way, AI has the potential to transform traditional actuarial methodologies and provide customized solutions for individual clients. In particular, the field of insurance has greatly benefited from the application of data science. With the use of data analytics, insurance companies can now develop predictive models to better manage risk, underwrite policies more accurately and determine valid pricing. Data science is also used to automate specific procedures such as claims processing, fraud detection, and customer retention. Insurance companies may use data science to identify and build new products that better match clients’ needs and preferences. In addition, the accessibility of data can improve operational efficiency by identifying areas of improvement and revenue-generating opportunities. Overall, the use of data science is quickly becoming a crucial aspect of the insurance industry, helping insurers improve their decision making, create new products and services and enhance custo

The special issue on Nonlinear Economic Dynamics contains a selection of papers presented at the 11th International Conference on Nonlinear Economic Dynamics (NED) that took place on September 4–6, 2019, at the Kyiv School of Economics, Ukraine. Organized under the auspices of the Nonlinear Economic Dynamics Society, the NED conference is a biennial (odd-year) international meeting of scholars interested in the development of methods for studying nonlinear dynamical systems and in their applications in economics and social sciences. The aim of this meeting is to bring together different streams of the growing literature in this field and to stimulate a fruitful exchange between theoretical research and applications in economics.

In this paper we leverage a massive attack-focused terrorist database and we design a dynamic bipartite network analysis to examine the structural evolution of terrorists-targets relationships. We introduce two novel measures to jointly assess harmfulness and vulnerability of terrorist and target groups, both at local and global level. Statistical validation using null models provides evidence that the information contained in these measures is new and not included in other variables, thus emphasizing the usefulness of these topological indicators. Finally, a policy-support experiment designed as network dismantling-like drill is proposed to assess the effects of potential attack preventive strategies.

The way agents form their expectations, and which equilibria are consequently selected, are issues that come over macroeconomic growth models that study the transition between states characterized by different levels of capital. Existing theoretical works in this area have been mostly dominated by perfect foresight models although alternative expectations schemes have been proposed in the last decades. In the present paper we propose an OLG model with capital accumulation assuming that agents employ simple yet heterogeneous rules to forecast the future course of the interest rate and the real wage. The forecasting rules are selected according to an evolutionary mechanism that, on the basis of a fitness measure, evaluates the performance of the heuristics agents are currently adopting. We analytically show that, in the heterogeneous setting we consider, multiple equilibria are possible, but the evolutionary heuristic switching allows for a decrease in the number of possible steady states, drives their selection, and reduces the actual possibility that the economy might be locked into a poverty trap.

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 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.

The market demand for the Treasury Inflation-Protected Securities (TIPS) is rather small. This is puzzling, as we show that an agent, who derives utility from real wealth and dynamically invests into multiple asset classes over a 30-year horizon, incurs a certainty equivalent loss of 1.6% per annum from not investing in inflation-indexed bonds. However, if the investor suffers from money illusion, the perceived loss is only 0.5% per annum. Furthermore, the perceived loss is totally negligible for an unsophisticated money-illusioned investor ignoring the time variation of risk premia. Money illusion causes significant portfolio shifts from inflation-indexed toward nominal bonds, with little effects on equity allocations, contributing to the low market demand for TIPS.

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment traders optimistically buy (pessimistically sell) a certain amount of stocks when the stock market is sufficiently rising (falling); otherwise they are inactive. As a result, the action of the price adjustment is represented by a map defined by three different functions, on three different partitions. This leads, in particular, to families of attracting cycles which are new with respect to those associated with a map defined on two partitions. We illustrate how to detect analytically the periodicity regions of these cycles considering the simplest cases of rotation number 1/n, n≥3, and obtaining in explicit form the bifurcation boundaries of the corresponding regions. We show that in the parameter space, these regions form two different overlapping period-adding structures that issue from the center bifurcation line. In particular, each point of this line, associated with a rational rotation number, is an issue point for two different periodicity regions related to attracting cycles with the same rotation number but with different symbolic sequences. Since these regions overlap with each other and with the domain of a locally stable fixed point, a characteristic feature of the map is multistability, which we describe by considering the corresponding basins of attraction. Our results contribute to the development of the bifurcation theory for discontinuous maps, as well as to the understanding of the excessively volatile boom-bust nature of stock markets.

In this paper we investigate the dynamics of a duopoly game with ambiguity aversion regarding uncertainty in demand and constant expectations concerning competitor production. The focus is on an asymmetric Cournot game where players engage in robust optimization and have different beliefs about the possible realizations of the random parameters of the price function. The players' ambiguity aversion introduces multiple equilibria and instability that otherwise would not be present. The investigation of the global dynamics of the game reveals the emergence, through border-collision bifurcations, of periodic and chaotic dynamics.

Dependence among different cyber risk classes is a fundamentally underexplored topic in the literature. However, disregarding the dependence structure in cyber risk management leads to inconsistent estimates of potential unintended losses. To bridge this gap, this article adopts a regulatory perspective to develop vine copulas to capture dependence. In quantifying the solvency capital requirement gradient for cyber risk measurement according to Solvency II, a dangerous paradox emerges: an insurance company does not tend to provide cyber risk hedging products as they are excessively expensive and would require huge premiums that it would not be possible to find policyholders.

In this paper, we aim at investigating various aspects of countries' behaviour during the coronavirus pandemic period. By means of a multiplex network, we simultaneously consider government responses based on COVID-19 infections, Stringency Index, international trade and international air mobility data, to detect clusters of countries that showed a similar reaction to the pandemic. We propose a new methodological approach based on the Estrada communicability for identifying communities on a multiplex network, based on a two-step optimization process. At first, we determine the optimal inter-layer weight between levels by minimizing a distance function. Hence, the optimal weight is used to detect the communities on each layer. Our findings show that this new approach to community detection on a multiplex network provides additional insights with respect to the same procedure performed on layers separately. Indeed, clusters in the multiplex network benefit from a higher cohesion, as they are detected taking into account the mutual influence of the other networks.