Since 2008, the network analysis of financial systems is one of the most important subjects in economics. In this paper, we have used the complexity approach and Random Matrix Theory (RMT) for analyzing the global banking network. By applying this method on a cross border lending network, it is shown that the network has been denser and the connectivity between peripheral nodes and the central section has risen. Also, by considering the collective behavior of the system and comparing it with the shuffled one, we can see that this network obtains a specific structure. By using the inverse participation ratio concept, we can see that after 2000, the participation of different modes to the network has increased and tends to the market mode of the system. Although no important change in the total market share of trading occurs, through the passage of time, the contribution of some countries in the network structure has increased. The technique proposed in the paper can be useful for analyzing different types of interaction networks between countries.

We use the Newcomb-Benford law to test if countries manipulate reported data during the COVID-19 pandemic. We find that democratic countries, countries with the higher Gross Domestic Product (GDP) per capita, higher healthcare expenditures, and better universal healthcare coverage are less likely to deviate from the Newcomb-Benford law. The relationship holds for the cumulative number of deaths and for the cumulative number of total cases but is more pronounced for the death toll. The findings are robust for the second digit tests, for a sub-sample of countries with regional data, and during the previous swine flu (H1N1) 2009-2010 pandemic.

Financial markets exhibit alternating periods of rising and falling prices. Stock traders seeking to make profitable investment decisions have to account for those trends, where the goal is to accurately predict switches from bullish towards bearish markets and vice versa. Popular tools for modeling financial time series are hidden Markov models, where a latent state process is used to explicitly model switches among different market regimes. In their basic form, however, hidden Markov models are not capable of capturing both short- and long-term trends, which can lead to a misinterpretation of short-term price fluctuations as changes in the long-term trend. In this paper, we demonstrate how hierarchical hidden Markov models can be used to draw a comprehensive picture of financial markets, which can contribute to the development of more sophisticated trading strategies. The feasibility of the suggested approach is illustrated in two real-data applications, where we model data from two major stock indices, the Deutscher Aktienindex and the Standard & Poor's 500.

Cryptocurrency refers to a type of digital asset that uses distributed ledger, or blockchain, technology to enable a secure transaction. Although the technology is widely misunderstood, many central banks are considering launching their own national cryptocurrency. In contrast to most data in financial economics, detailed data on the history of every transaction in the cryptocurrency complex are freely available. Furthermore, empirically-oriented research is only now beginning, presenting an extraordinary research opportunity for academia. We provide some insights into the mechanics of cryptocurrencies, describing summary statistics and focusing on potential future research avenues in financial economics.

The objective of this paper is to develop a duality between a novel Martingale Entropy Optimal Transport problem (D) and an associated optimization problem (P). In (D) we follow the approach taken in the Entropy Optimal Transport (EOT) primal problem by (Liero et al. "Optimal entropy-transport problems and a new Hellinger-Kantorovic distance between positive measures", Invent. math. 2018) but we add the constraint, typical of Martingale Optimal Transport (MOT) theory, that the infimum of the cost functional is taken over martingale probability measures, instead of finite positive measures, as in Liero et al. The Problem (D) differs from the corresponding problem in Liero et al. not only by the martingale constraint, but also because we admit less restrictive relaxation terms D, which may not have a divergence formulation. In Problem (P) the objective functional, associated via Fenchel coniugacy to the terms D, is not any more linear, as in OT or in MOT. This leads to a novel optimization problem which also has a clear financial interpretation as a non linear subhedging value. Our results allow us to establish a novel nonlinear robust pricing-hedging duality in financial mathematics, which covers a wide range of known robust results in its generality.

We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of 'lockdown' to reduce the number of new infections. Specifically we use a collisional approach to an infection-age structured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical proximity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distancing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interactions among people, which may help policy makers to improve remote-working organizational structure.

In this study, we investigate the flow of money among bank accounts possessed by firms in a region by employing an exhaustive list of all the bank transfers in a regional bank in Japan, to clarify how the network of money flow is related to the economic activities of the firms. The network statistics and structures are examined and shown to be similar to those of a nationwide production network. Specifically, the bowtie analysis indicates what we refer to as a "walnut" structure with core and upstream/downstream components. To quantify the location of an individual account in the network, we used the Hodge decomposition method and found that the Hodge potential of the account has a significant correlation to its position in the bowtie structure as well as to its net flow of incoming and outgoing money and links, namely the net demand/supply of individual accounts.In addition, we used non-negative matrix factorization to identify important factors underlying the entire flow of money; it can be interpreted that these factors are associated with regional economic activities.One factor has a feature whereby the remittance source is localized to the largest city in the region, while the destination is scattered. The other factors correspond to the economic activities specific to different local places.This study serves as a basis for further investigation on the relationship between money flow and economic activities of firms.

Microlending, where a bank lends to a small group of people without credit histories, began with the Grameen Bank in Bangladesh, and is widely seen as the creation of Muhammad Yunus, who received the Nobel Peace Prize in recognition of his largely successful efforts. Since that time the model of microlending has received a fair amount of academic attention. One of the issues not yet addressed in detail, however, is the issue of the size of the group. (Some attention has nevertheless been paid, see the appropriate references in this paper.) Instead of a game theory approach, we take a mathematical approach to the issue of an optimal group size, where the goal is to minimize the probability of default of the group. To do this, one has to create a model with interacting forces, and to make precise the hypotheses of the model. (In previous work we have addressed the issue of what is a fair rate of interest to charge for such a loan.) We show that the original choice of Muhammad Yunus, of a group size of five people, is, under the right (and, we believe, reasonable) hypotheses, either close to optimal, or even at times exactly optimal, i.e., the optimal group size is indeed five people.

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.

Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the "instantaneous arbitrage capability" generated by the market itself. The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market allowing for arbitrage. Results, obtained by solving explicitly the Schr\"odinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency.