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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.

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.

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.

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. (c) 2022 Elsevier B.V. All rights reserved.

Within the insurance field, the digital revolution has enabled the collection and storage of large quantities of information [...]

Let $Y$ be a subspace of a topological vector space $X$, and $A\subset X$ an open convex set that intersects $Y$. We say that the property $(QE)$ [property $(CE)$] holds if every continuous quasiconvex [continuous convex] function on $A\cap Y$ 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 \cite{DEQEX} to the infinite-dimensional separable case. Moreover, we also immediately obtain existence of examples in which $(QE)$ does not hold.

Let us consider two sequences of closed convex sets $\{A_n\}$ and $\{B_n\}$ converging with respect to the Attouch-Wets convergence to $A$ and $B$, respectively. Given a starting point $a_0$, we consider the sequences of points obtained by projecting on the "perturbed" sets, i.e., the sequences $\{a_n\}$ and $\{b_n\}$ defined inductively by $b_n=P_{B_n}(a_{n-1})$ and $a_n=P_{A_n}(b_n)$. Suppose that $A\cap B$ (or a suitable substitute if $A \cap B=\emptyset$) is bounded, we prove that if the couple $(A,B)$ is (boundedly) regular then the couple $(A,B)$ is $d$-stable, i.e., for each $\{a_n\}$ and $\{b_n\}$ as above we have $\mathrm{dist}(a_n,A\cap B)\to 0$ and $\mathrm{dist}(b_n,A\cap B)\to 0$., Comment: 16 pages. arXiv admin note: text overlap with arXiv:1907.13402

The paper considers the pricing of credit default swaps (CDSs) using a revised version of the credit risk model proposed in Cathcart and El-Jahel (2003). Default occurs either the first time a signaling process breaches a threshold barrier or unexpectedly at the first jump of a Cox process. The intensity of default depends on the risk-free interest rate, which follows a Vasicek process, instead of a Cox-Ingersoll-Ross process as in the original model. This offers two advantages. On the one hand, it allows us to account for negative interest rates which are recently observed, on the other hand, it simplifies the formula for pricing CDSs. The goodness of fit of the model is tested using a dataset of CDS credit spreads related to European companies. The results obtained show a rather satisfactory agreement between theoretical predictions and market data, which is identical to the one obtained with the original model. In addition, the values of the calibrated parameters result to be stable over time and the semi-closed form solution ensures a very fast implementation.

The critical price $$S^{*}\left( t\right) $$ S ∗ t of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that $$S^{*}\left( t\right) $$ S ∗ t coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals $$S^{*}\left( t\right) $$ S ∗ t ’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of $$S^{*}\left( t\right) $$ S ∗ t and rigorously show the correspondence of an American option problem to an easier European option problem at maturity .

In this work we reconsider the dynamics of a few versions of the classical Samuelson's multiplier- accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate oscillations con- verging to the equilibrium for a wide range of values of the parameters, and give its analytic solution for all the possible cases. A delayed version proposed in the recent literature, represented by a linear third-order di¤erence equation, is also considered. We show that also this model is able to produce converging oscilla- tions, and give a complete analysis of the stability region of the equilibrium. A new simple nonlinear model is proposed, showing that it keeps oscillatory behavior, although coupled with other dynamics related to global effects. Our analysis confirms that the seminal work of Samuelson and simple modifications of it, may give powerful tools in the study of the business cycles.

Assortativity by degree for complex networks is quantified by the Newman coefficient, and it describes a tendency for nodes to be connected to others with a similar degree. A generalization of the assortativity index has been proposed in the literature for undirected and unweighted networks, analysing the correlation between vertices that are not necessarily adjacent, but connected through paths, shortest paths and random walks. The aim of this study is to define a new class of higher-order assortativity measures for weighted networks. The effectiveness of these measures is evident in social networks, where both weights and connections are significant. Applications to Facebook and co-authorship networks are provided, analysing the assortativity beyond the nearest neighbours.

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.

We reconsider the well-known conditions which guarantee the roots of a third-degree polynomial to be inside the unit circle. These conditions are important in the stability analysis of equilibria a...

Residential segregation is a key public policy issue that is driven by economic factors on the one side, and individual attitudes towards ethnic diversity on the other side. We assume a modeling framework that consists of a population of two ethnic groups, a rental market for each neighborhood, and household's utility which depends on consumption and housing. Accounting for income disparities and heterogeneous preferences for living in ethnically diverse neighborhoods, we examine the residential segregation patterns that occur when households make their neighborhood choice by taking economic and diversity related aspects into account. The investigation reveals that ethnic income disparities and heterogeneous preferences are antagonistic forces such that a certain level of income stratification is the price for residential integration. In light of these findings, we discuss to which extent and under which conditions housing subsidy policies can favor residential integration. (c) 2020 Elsevier B.V. All rights reserved.

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.

Loss portfolio transfer (LPT) is a reinsurance treaty in which an insurer cedes the policies that have already incurred losses to a reinsurer. This operation can be carried out by an insurance company in order to reduce reserving risk and consequently reduce its capital requirement calculated, according to Solvency II. From the viewpoint of the reinsurance company, being a very complex operation, importance must be given to the methodology used to determine the price of the treaty.Following the collective risk approach, the paper examines the risk profiles and the reinsurance pricing of LPT treaties, taking into account the insurance capital requirements established by European law. For this purpose, it is essential to calculate the capital need for the risk deriving from the LPT transaction. In the case analyzed, this requirement is calculated under Solvency II legislation, considering the measure of variability determined via simulation. This quantification was also carried out for different levels of the cost of capital rate, providing a range of possible loadings to be applied to the premium. In the case of the Cost of Capital (CoC) approach, the results obtained provide a lower level of premium compared to the percentile-based method with a range between 2.69% and 1.88%. Besides, the CoC approach also provides the advantage of having an explicit parameter, the CoC rate whose specific level can be chosen by the reinsurance company based on the risk appetite.

One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

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.

In this work we analyse the global soccer player transfer market providing a network approach that takes into account both the number of transfers and the related costs for football players in the world market. We propose a community detection methodology that considers different features of the network. We cluster countries according to similarities in their roles in the transfer market and to the presence of indirect connections due to common neighbours. Numerical results show a strict relation between the composition of clusters and the economic value of the football leagues of different countries. Indeed, we observe that, on average, leagues with a similar economic value belongs to the same cluster. The analysis has been also extended providing a comparison based on the world trade network. We observe that prominent European players in the economic trades are also relevant in the soccer transfer network.

Life insurance profitability depends on reliable mortality risk projections and pricing. While the COVID-19 pandemic has caused disruptions around the world, this is a temporary mortality shock likely to dissipate. In this paper, we investigate the long-run impact of COVID-19 on life insurance profitability. Due to the long-run dynamics of the mortality characterised by a decreasing effect of the COVID-19 mortality acceleration, we suggest proactive mortality risk management by implementing prompt premium adjustments, in order to increase the resilience of the business.

This paper analyzes the asset pricing and portfolio implications of an important barrier to sustainable investing: uncertainty about the corporate ESG profile. In equilibrium, the market premium increases and demand for stocks declines under ESG uncertainty. In addition, the CAPM alpha and effective beta both rise with ESG uncertainty and the negative ESG-alpha relation weakens. Employing the standard deviation of ESG ratings from six major providers as a proxy for ESG uncertainty, we provide supporting evidence for the model predictions. Our findings help reconcile the mixed evidence on the cross-sectional ESG-alpha relation and suggest that ESG uncertainty affects the risk-return trade-off, social impact, and economic welfare.

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.

We suggest a new, parsimonious, method to fit financial data with a stable distribution. As a result of a stable fitting via maximum likelihood estimation (MLE), we find that some assets have similar values as stability indices, independently of the time interval considered. This fact can be exploited to pool the assets in groups and to choose a parameter $$\alpha $$ as an ex ante stability index, valid for every asset in the pool sector. With this fixed parameter, MLE is used again to obtain the other stable parameters. We discuss an innovative risk measure, based on the Expected Shortfall, which exploits the above procedure. We show that it gives a good estimation of risk even when only short time series are available. Finally, we introduce the notion of Risk Class, which allows us to classify assets according to their risk exposition and to compare different methods for the computation of the Expected Shortfall.

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.

This work investigates financial volatility cascades generated by SARS-CoV-2 related news using concepts developed in the field of seismology. We analyze the impact of socio-economic and political announcements, as well as of financial stimulus disclosures, on the reference stock markets of the United States, United Kingdom, Spain, France, Germany and Italy. We quantify market efficiency in processing SARS-CoV-2 related news by means of the observed Omori power-law exponents and we relate these empirical regularities to investors’ behavior through the lens of a stylized Agent-Based financial market model. The analysis reveals that financial markets may underreact to the announcements by taking a finite time to re-adjust prices, thus moving against the efficient market hypothesis. We observe that this empirical regularity can be related to the speculative behavior of market participants, whose willingness to switch toward better performing investment strategies, as well as their degree of reactivity to price trend or mispricing, can induce long-lasting volatility cascades.

There have been some recent attempts to combine Cournot and Bertrand duopolies in one single model. Unfortunately, these attempts do not work. A commodity cannot be homogenous and non-homogenous at the same time. It is always the consumers, who decide whether they perceive competing products as identical or as different brands for which they are willing to pay different prices. There is, of course, nothing that forbids the coexistence of both such consumer groups. Neither is there any obstacle for the competing sellers to sell to both markets. Then we only need an old idea from economic theory, i.e., price discrimination, to rectify the logic. By this the challenging combination idea comes on a stable footing. The model also results in some interesting mathematical facts, such as mulistability and coexistence of attractors.