Controlling systemic risk: Network structures that minimize it and node properties to calculate it.

Evaluation of systemic risk in networks of financial institutions in general requires information of interinstitution financial exposures. In the framework of the DebtRank algorithm, we introduce an approximate method of systemic risk evaluation which requires only node properties, such as total assets and liabilities, as inputs. We demonstrate that this approximation captures a large portion of systemic risk measured by DebtRank. Furthermore, using Monte Carlo simulations, we investigate network structures that can amplify systemic risk. Indeed, while no topology in general sense is a priori more stable if the market is liquid (i.e., the price of transaction creation is small) [T. Roukny et al., Sci. Rep. 3, 2759 (2013)10.1038/srep02759], a larger complexity is detrimental for the overall stability [M. Bardoscia et al., Nat. Commun. 8, 14416 (2017)10.1038/ncomms14416]. Here we find that the measure of scalar assortativity correlates well with level of systemic risk. In particular, network structures with high systemic risk are scalar assortative, meaning that risky banks are mostly exposed to other risky banks. Network structures with low systemic risk are scalar disassortative, with interactions of risky banks with stable banks.

Repulsion in controversial debate drives public opinion into fifty-fifty stalemate.

Opinion formation is a process with strong implications for public policy. In controversial debates with large consequences, the public opinion is often trapped in a fifty-fifty stalemate, jeopardizing broadly accepted political decisions. Emergent effects from millions of private discussions make it hard to understand or influence this kind of opinion dynamics. Here we demonstrate that repulsion from opinions favors fifty-fifty stalemates. We study a voter model where agents can have two opinions or an undecided state in between, and where we allow for repulsion of opinions and for doubt: in pairwise discussions, undecided agents can be not only convinced, but also repelled from the opinion expressed by another agent, and decided agents may return to the undecided state. As a result, we observe that, if an agent is repelled instead of being convinced in at least one out of four interactions, as in controversial debates, the frequencies of both opinions equalize. This voter model attractor reproduces the phenomenology of repeated Brexit poll data well and provides a mechanism solely based on local interactions between agents that may explain stalemate polarization in controversial opinion formation.

Impact and recovery process of mini flash crashes: An empirical study.

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not necessarily due to feedbacks in High Frequency Trading: In at least 60 percent of the observed Ultrafast Extreme Events, the largest fraction of the price change is due to a single market order. In times of financial crisis, large market orders are more likely which leads to a significant increase of Ultrafast Extreme Events occurrences. Furthermore, we analyze the 100 trades following each Ultrafast Extreme Events. While we observe a tendency of the prices to partially recover, less than 40 percent recover completely. On the other hand we find 25 percent of the Ultrafast Extreme Events to be almost recovered after only one trade which differs from the usually found price impact of market orders.

Color-avoiding percolation.

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in S. M. Krause et al. [Phys. Rev. X 6, 041022 (2016)]2160-330810.1103/PhysRevX.6.041022. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. Here we propose a better method for solving this problem which is substantially more accurate for many avoided colors. Further, we formulate our method with differentiated node functions, either as senders and receivers, or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. Avoiding additional colors one by one, we can understand the critical behavior of color-avoiding percolation. For unequal color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color-avoiding connectivity, thus allowing for approximations.

Econophysics of adaptive power markets: When a market does not dampen fluctuations but amplifies them.

The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of a system of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as, e.g., wind or solar) via a market mechanism, namely by variable power prices that adapt demand to supply. The standard model of an average economic agent predicts that fluctuations are reduced by such an adaptive pricing mechanism. However, the underlying assumption that the actions of all agents average out on the time axis is not always true in a market of many agents. We numerically study an econophysics agent model of an adaptive power market that does not assume averaging a priori. We find that when agents are exposed to source noise via correlated price fluctuations (as adaptive pricing schemes suggest), the market may amplify those fluctuations. In particular, small price changes may translate to large load fluctuations through catastrophic consumer synchronization. As a result, an adaptive power market may cause the opposite effect than intended: Power demand fluctuations are not dampened but amplified instead.

Spontaneous centralization of control in a network of company ownerships.

We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected "core" made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive "rich get richer" dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.

Opinion formation model for markets with a social temperature and fear.

In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the two-dimensional voter model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents toward market imbalances representing speculative risk. We use the knowledge about the discontinuous generalized voter model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized, and its relation to dynamics of opinion formation among investors in real markets is discussed.

Mean-field-like behavior of the generalized voter-model-class kinetic Ising model.

We analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the context of social systems and opinion formation in the presence of a tunable social temperature. On the other hand, we characterize the abrupt phase transition. The system shows nonequilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary-state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean-field calculations, we investigate the phase transition, finite-size effects, and the effect of the absorbing states resulting in a dynamic slowing down.