We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean--Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean--Vlasov problem, which can be realised as limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise.

We address the modelling of commodities that are supposed to have positive price but, on account of a possible failure in the physical delivery mechanism, may turn out not to. This is done by explicitly incorporating a `delivery liability' option into the contract. As such it is a simple generalisation of the established Black model.

In this study, we extend the research on the dynamic poverty indexes, namely the dynamic Headcount ratio, the dynamic income-gap ratio, the dynamic Gini and the dynamic Sen, proposed in D'Amico and Regnault (2018). The contribution is twofold. First, we extend the computation of the dynamic Gini index, thus the Sen index accordingly, with the inclusion of the inequality within each class of poverty where people are classified according to their income. Second, for each poverty index, we establish a central limit theorem that gives us the possibility to determine the confidence sets. An application to the Italian income data from 1998 to 2012 confirms the effectiveness of the considered approach and the possibility to determine the evolution of poverty and inequality in real economies.

Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on chance?

We show the answer is yes by describing two nondeterministic voting methods, one based on automatic bargaining over lotteries, the other on conditional commitments to approve compromise options. Our theoretical analysis and agent-based simulation experiments suggest that with these, majorities cannot consistently suppress minorities as with deterministic methods, proponents of the status quo cannot block decisions as in consensus-based approaches, the resulting aggregate welfare is comparable to existing methods, and average randomness is lower than for other nondeterministic methods.

At the end of 2012 the International Monetary Fund (IMF) has suspended its financial assistance to the Democratic Republic of the Congo (DRC). Due to inflationary pressures which occurred in the last quarter of 2016, several decision-makers called for a reopening of a formal cooperation with the IMF. This process was formally completed in December 2019. The restart of IMF programs was greeted with satisfaction by politicians and widely commented in the media. However, recent history shows that the DRC managed to achieve exceptional economic performance, between 2012 and 2016, without being in a formal cooperation with the IMF. Some people wonder whether IMF assistance is a curse for recipient countries? We argue that the underlying problem has nothing to do with accepting or not the IMF assistance, but rather in the ability of policy makers to establish effective leadership and good governance for the development and implementation supporting structural reforms.

Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. It was hypothesized that this optimal leverage is attracted to 1, such that, e.g., leveraging an investment in the market portfolio cannot yield long-term outperformance. This places a strong constraint on the stochastic properties of prices of traded assets, which we call "leverage efficiency." Market conditions that deviate from leverage efficiency are unstable and may create leverage-driven bubbles. Here we expand on the hypothesis and its implications. These include a theory of noise that explains how systemic stability rules out smooth price changes at any pricing frequency; a resolution of the so-called equity premium puzzle; a protocol for central bank interest rate setting to avoid leverage-driven price instabilities; and a method for detecting fraudulent investment schemes by exploiting differences between the stochastic properties of their prices and those of legitimately-traded assets. To submit the hypothesis to a rigorous test we choose price data from different assets: the S&P500 index, Bitcoin, Berkshire Hathaway Inc., and Bernard L. Madoff Investment Securities LLC. Analysis of these data supports the hypothesis.

Homeowners around the world elevate houses to manage flood risks. Deciding how high to elevate the house poses a nontrivial decision problem. The U.S. Federal Emergency Management Agency (FEMA) recommends elevating existing houses to the Base Flood Elevation (the elevation of the 100-yr flood) plus a freeboard. This recommendation neglects many uncertainties. Here we analyze a case-study of riverine flood risk management using a multi-objective robust decision-making framework in the face of deep uncertainties. While the quantitative results are location-specific, the approach and overall insights are generalizable. We find strong interactions between the economic, engineering, and Earth science uncertainties, illustrating the need for expanding on previous integrated analyses to further understand the nature and strength of these connections. We show that considering deep uncertainties surrounding flood hazards, the discount rate, the house lifetime, and the fragility increases the economically optimal house elevation to values well above FEMA recommendation.

This paper uses a mathematical model with appropriate assumptions, to model and to determine the optimal group size for microfinance loans. An optimal size is defined to be the size which maximizes the probability of no default of the group

We consider an auction type equilibrium model with an insider in line with the one originally introduced by Kyle in 1985 and then extended to the continuous time setting by Back in 1992. The novelty introduced with this paper is that we deal with a general price functional depending on the whole past of the aggregate demand, i.e. we work with path-dependency. By using the functional It\^o calculus, we provide necessary and sufficient conditions for the existence of an equilibrium. Furthermore, we consider both the cases of a risk-neutral and a risk-averse insider.

Towards the realization of a sustainable, fair and inclusive society, we proposed a novel decision-making model that incorporates social norms in a rational choice model from the standpoints of deontology and utilitarianism. We proposed a hypothesis that interprets choice of action as the X-point for individual utility function that increases with actions and social norm function that decreases with actions. This hypothesis is based on humans psychologically balancing the value of utility and norms in selecting actions. Using the hypothesis and approximation, we were able to isolate and infer utility function and norm function from real-world measurement data of actions on environmental conditions and elucidate the interaction between the both functions that led from current status to target actions. As examples of collective data that aggregate decision-making of individuals, we looked at the changes in power usage before and after the Great East Japan Earthquake and the correlation between national GDP and CO2 emission in different countries. The first example showed that the perceived benefits of power (i.e., utility of power usage) was stronger than the power usage restrictions imposed by norms after the earthquake, contrary to our expectation. The second example showed that a reduction of CO2 emission in each country was not related to utility derived from GDP but to norms related to CO2 emission. Going forward, we will apply this new X-point model to actual social practices involving normative problems, and design the approaches for the diagnosis, prognosis and intervention of social systems by IT systems.

In this paper, we investigate whether mixing cryptocurrencies to a German investor portfolio improves portfolio diversification. We analyse this research question by applying a (mean variance) portfolio analysis using a toolbox consisting of (i) the comparison of descriptive statistics, (ii) graphical methods and (iii) econometric spanning tests. In contrast to most of the former studies we use a (broad) customized, Equally-Weighted Cryptocurrency Index (EWCI) to capture the average development of a whole ex ante defined cryptocurrency universe and to mitigate possible survivorship biases in the data. According to Glas/Poddig (2018), this bias could have led to misleading results in some already existing studies. We find that cryptocurrencies can improve portfolio diversification in a few of the analyzed windows from our dataset (consisting of weekly observations from 2014-01-01 to 2019-05-31). However, we cannot confirm this pattern as the normal case. By including cryptocurrencies in their portfolios, investors predominantly cannot reach a significantly higher efficient frontier. These results also hold, if the non-normality of cryptocurrency returns is considered. Moreover, we control for changes of the results, if transaction costs/illiquidities on the cryptocurrency market are additionally considered.

Behavioral responses to pandemics are less shaped by actual mortality or hospitalization risks than they are by risk attitudes. We explore human mobility patterns as a measure of behavioral responses during the COVID-19 pandemic. Our results indicate that risk-taking attitude is a critical factor in predicting reduction in human mobility and increase social confinement around the globe. We find that the sharp decline in movement after the WHO (World Health Organization) declared COVID-19 to be a pandemic can be attributed to risk attitudes. Our results suggest that regions with risk-averse attitudes are more likely to adjust their behavioral activity in response to the declaration of a pandemic even before most official government lockdowns. Further understanding of the basis of responses to epidemics, e.g., precautionary behavior, will help improve the containment of the spread of the virus.

In a world increasingly dominated by AI applications, an understudied aspect is the carbon and social footprint of these power-hungry algorithms that require copious computation and a trove of data for training and prediction. While profitable in the short-term, these practices are unsustainable and socially extractive from both a data-use and energy-use perspective. This work proposes an ESG-inspired framework combining socio-technical measures to build eco-socially responsible AI systems. The framework has four pillars: compute-efficient machine learning, federated learning, data sovereignty, and a LEEDesque certificate.

Compute-efficient machine learning is the use of compressed network architectures that show marginal decreases in accuracy. Federated learning augments the first pillar's impact through the use of techniques that distribute computational loads across idle capacity on devices. This is paired with the third pillar of data sovereignty to ensure the privacy of user data via techniques like use-based privacy and differential privacy. The final pillar ties all these factors together and certifies products and services in a standardized manner on their environmental and social impacts, allowing consumers to align their purchase with their values.

In a refreshing mathematical investigation, Mark (2018) shows that status hierarchy may facilitate the emergence of cooperation in groups. Despite the contribution, the present paper notes that there are limitations in Mark's model that makes it less realistic than it could in explaining real-world experiences. Consequently, we present a more generalized modified framework in which his model is a special case, by developing and introducing a new hierarchy measure into the model to estimate the cooperation level in a set of hierarchical structures omitted in Mark's work yet common in everyday life--those with multiple leaders. We derived the conditions under which cooperation can emerge in these groups, and verified our analytical predictions in agent-based computer simulations. In so doing, not only does our model elaborate on its predecessor and support Mark's general prediction. For theory, our work further reveals two novel phenomena of group cooperation: Both the relative number of cooperators to defectors in groups and the assortativity among these different roles can backfire; they are not always the higher, the better for cooperation to thrive. For methodology, the hierarchy measure developed and our model using the measure may also be applied in future research on a wide range of related topics.

We consider the possibility of social and economical collapse of population caused by epidemics. We exploit a simplest toy model with negative feedback for the dynamics of epidemic spreading in population with its mutual influence on some formal resource (economical, financial, etc). For epidemics spreading we use the simple SIS model, supplemented with the simplest equation for the dynamics of the resource whose generation is determined by the active labor resource. We note that the patient's characteristic rehabilitation rate or recovery time depends on the cost of health services, cost of the bare subsistence level of consumption, $E$, and the availability of some formal resource $\rho$, e.g. money. Since the cost of services is fixed, the service is terminated if there is not enough personal, private, or collective financial resource $\rho\ll E$, the service is absent. Therefore, we suppose that recovery rate should have an activation character $\sim\exp(-E/\rho)$. We show that depending on the rate of epidemics spreading and on the availability of formal resource, the system can come back to normal life, can overcome the stress or move to another stable but more "poor" state. Otherwise, the system can collapse. While collapsing, the system can pass through a number of quasi-stable states, its dynamics being resembling the so-called devil's staircase.