Causal Hierarchy in the Financial Market Network-Uncovered by the Helmholtz-Hodge-Kodaira Decomposition.

Granger causality can uncover the cause-and-effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into rotational and gradient components which reveal the hierarchy of the Granger causality flow. Using Kenneth French's business sector return time series, it is revealed that during the COVID crisis, precious metals and pharmaceutical products were causal drivers of the financial network.

Cooperation in a non-ergodic world on a network - insurance and beyond.

Cooperation between individuals is emergent in all parts of society; yet, mechanistic reasons for this emergence are ill understood in the literature. A specific example of this is insurance. Recent work has, though, shown that assuming the risk individuals face is proportional to their wealth and optimizing the time average growth rate rather than the ensemble average results in a non-zero-sum game, where both parties benefit from cooperation through insurance contracts.

Estimating stable fixed points and Langevin potentials for financial dynamics.

The geometric Brownian motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalizes the GBM to an SDE with polynomial drift of order q and shows via model selection that q=2 is most frequently the optimal model to describe the data. Moreover, Markov chain Monte Carlo ensembles of the accompanying potential functions show a clear and pronounced potential well, indicating the existence of a stable price.

Efficient Multi-Change Point Analysis to Decode Economic Crisis Information from the S&P500 Mean Market Correlation.

Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understanding the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis, which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis, and the Euro crisis.

Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation.

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500, which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks.

Quantifying resilience and the risk of regime shifts under strong correlated noise.

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio.

Anticipating the occurrence and type of critical transitions.

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition.

Adaptive stochastic continuation with a modified lifting procedure applied to complex systems.

Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models.

Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input.

Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids, and this becomes an important risk factor for maintaining power grid stability. Here, we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an Institute of Electrical and Electronics Engineers test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of 1 min.

Instability threshold of a photorefractive pattern-forming system.

We report on the detailed experimental determination of the threshold for modulational instability in a photorefractive single-mirror feedback system using a Fourier control technique. Results are compared to analytical predictions and a disagreement for the experimentally significant multiple pattern region is found. Implications for the generation of nonhexagonal two-dimensional patterns are discussed.