This paper uses MIS to identify key financial institutions with minimal risk contagion.
problem Mitigating systemic risk during extreme financial events.
method Applying extreme value theory and MIS from graph theory to identify diversified portfolios.
result Identified a subset of institutions with minimal extremal dependence for diversified portfolios.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
problem Characterizing extremals in sub-Lorentzian structures.
method Deriving Hamiltonian system and conditions for extremal trajectories.
result Conditions for normal extremal trajectories and properties of abnormal extremals.
Extremely accurate prediction of dynamical system bifurcations using control inputs.
problem Predicting complex bifurcation structures in dynamical systems.
method Extending extreme learning machines with control inputs to model system dynamics.
result The model can nearly reproduce the entire structure of bifurcations using only a few parameter values.
We develop a framework for analyzing extreme values in correlated financial data.
problem Quantifying and mitigating risk in complex financial systems.
method Developed a practical framework for handling finite, multivariate, and correlated time series in finance.
result We successfully analyze high-frequency stock returns using univariate extreme value tools.
Deep learning models learn chaotic system dynamics from real and simulated data.
problem Training deep learning models for chaotic systems requires big data.
method Jointly train deep neural networks on real and simulated data, enforcing physical laws.
result Proposes knowledge-based deep learning (KDL) for accurate forecasting of chaotic systems.
The paper proves extremal black holes form at a critical point of gravitational collapse.
problem Formation of extremal black holes in gravitational collapse.
method Constructing smooth families of spherically symmetric solutions to the Einstein-Maxwell-Vlasov system.
result Extremal Reissner-Nordström black holes form at the critical collapse threshold.
xVAE models extreme turbulence events in turbulent flows.
problem Capturing extreme events in turbulent flows.
method Max-infinitely divisible process with heavy-tailed distributions embedded into a standard VAE framework.
result xVAE more robust in capturing extreme values compared to POD modes.
New method forecasts systemic risk with improved precision.
problem Improving the estimation of systemic risk measures.
method De-volatilizing observations and using extreme value theory for forecasting.
result Valid MES forecasts with good coverage in simulations and empirical applications.
The study measures systemic risk using common and tail dependence factors.
problem Measuring systemic risk accurately during economic downturns.
method Modeling systemic risk with a common factor for market-wide shocks and a tail dependence factor for extreme events.
result Measures including a tail dependence factor offer better forecasting of financial stress than measures based solely on a common factor.
New method simulates multivariate extreme events using GANs and Aitchison coordinates.
problem Simulating multivariate extreme events for economic risk assessment.
method Wasserstein-Aitchison GAN approach combining tail dependence and marginal tail modeling.
result Strong performance in capturing tail dependence and generating accurate extreme observations.
In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of nonlinear geodesic equations. Particularly, we investigate the light-like extremal su…
Study extremals on Lie groups with asymmetric polyhedral Finsler structures using Pontryagin's Maximal Principle.
problem Finding extremals on Lie groups with asymmetric polyhedral Finsler structures.
method Using Pontryagin's Maximal Principle and control systems of Euler-Arnold type to find extremals on the cotangent bundle of the group.
result Uniqueness of the control u(t) can be studied through the asymptotic curvature of the vertical part of the Pontryagin extremal. AI-assisted framework detects and predicts rare extreme events.
problem Detecting rare extreme events in complex systems.
method Combining BED with DNOs for active learning and forecasting.
result Framework outperforms GPs and uncovers extremes without initial data.
Researchers solved a problem about extreme mass distributions in quasi-copulas.
problem Solving the extreme mass distribution problem for quasi-copulas.
method Analytical approach using linear programming.
result Complete solution to the original problem, disproving a conjecture.
Recently, large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of the self-organized criticality (SOC). Recent empirical work has suggested that some extreme events systematically deviate from the SOC paradigm, requiring a diffe…
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.
ML models predict extreme events in the Hénon map with accuracy scaling with system parameters.
problem Predicting extreme events in chaotic dynamical systems like the Hénon map.
method Used machine learning algorithms to analyze and forecast extreme events in the Hénon map.
result The success rate of ML models depends on prediction time, number of training samples, and network size, with scaling relations to the system's topological entropy.
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the 'next-best' data point (set of parameters) that when evaluated results in improv…
Investigates how options can control systemic risk in portfolios.
problem Systemic risk in optioned portfolios.
method Correlation hedging, extreme loss hedging, and SOCP formulation.
result Options can make systemic risk controllable and enhance return-risk performance.
Method identifies financial rogue waves close to their onset.
problem Identifying extreme financial events close to their onset.
method Analogy between rogue waves in optics and financial volatility, using Schrödinger equation with potential shaped by Kerr nonlinearity.
result Numerical gradient spikes at the onset of extreme financial events.
Framework reconstructs missing spatio-temporal data for extreme value prediction.
problem Predicting extreme values from incomplete spatio-temporal data.
method Convolutional deep neural networks and autoencoder-like models for conditional sampling.
result Framework produces accurate reconstructions of missing data for extremal values.
A new algorithm for selecting top-k arms in extreme contextual bandits with improved efficiency.
problem Selecting top-k arms from a large set with contextual information and limited rewards.
method Proposes an algorithm for both non-extreme and extreme settings, using Inverse Gap Weighting and arm hierarchy models.
result Achieves improved regret guarantees for extreme settings with significant computational and statistical efficiency.
Study proves curvature estimates for Kerr spacetime's linearized perturbations.
problem Proving elliptic L2(S2)-estimates for linearised curvature quantities in Kerr spacetime. method Applies linearised system from doctoral thesis, covers full sub-extremal range of Kerr parameters.
result Elliptic L2(S2)-estimates for linearised curvature quantities in the full sub-extremal range of Kerr parameters. A new method reduces uncertainty in predicting rare extreme events without assuming their presence in training data.
problem Predicting rare and extreme events in complex systems with high uncertainty.
method Extreme Event Aware (e2a or η) learning, which enforces extreme event statistics during training.
result Models generate unprecedented extreme events even when training data lacks extremes.
New test identifies risk spillovers in financial markets using extreme events.
problem Identifying risk spillovers in financial markets for systemic risk assessment.
method Novel Granger causality test in tail events using likelihood ratio statistic.
result Good size and power, especially for large sample size, inferring correct time scale.
We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry o…
The article models financial asset returns using Gaussian mixtures and EVT-based copulas to price equity options.
problem Modeling financial asset returns and pricing equity options considering extreme values.
method Modeling marginal distributions with Gaussian mixtures and joint dependence structure with EVT-based copulas.
result The approach accurately prices various equity options on Atos and Dassault Systems actions.
Modeling house prices in Australia reveals supply limitations as the primary driver of extreme trends.
problem Understanding the resilience of Australia's housing prices despite changes in mortgage rates.
method Developed a differential equation model and used modern extreme value techniques on real-world data.
result Without supply increases, a 11% mortgage rate hike is needed to moderate extreme housing costs.
Neural network model forecasts extreme flood risk.
problem Accurately estimating high quantiles of extreme events.
method EQRN model combining neural networks and extreme value theory.
result Forecasting flood risk with improved adaptability.
In this paper, we develop an online method that leverages machine learning to obtain feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps on extremely fast timescales (e.g., milliseconds), bypassing solving an AC OPF altogether. This is motivated by the fact that as the power gr…
Natural disasters can have catastrophic impacts on the functionality of infrastructure systems and cause severe physical and socio-economic losses. Given budget constraints, it is crucial to optimize decisions regarding mitigation, preparedness, response, and recovery practices for these systems. This requires accurate…
We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that …
A characteristic feature of complex systems in general is a tight coupling between their constituent parts. In complex socio-economic systems this kind of behavior leads to self-organization, which may be both desirable (e.g. social cooperation) and undesirable (e.g. mass panic, financial "bubbles" or "crashes"). Abund…
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved using separating transformations and learning functions in detail. Methods used …
We prove boundedness and polynomial decay statements for solutions to the spin ±2 generalized Teukolsky system on a Reissner-Nordström background with small charge. The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $…
The paper classifies electrovacuum spaces in higher dimensions, proving several key results.
problem Classifying regular static black hole solutions of the static Einstein-Maxwell equations.
method Analytical proofs and geometric analysis of electrovacuum spaces.
result An n-dimensional locally conformally flat extremal electrovacuum space must be in the Majumdar-Papapetrou class.
Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.
Model uses Navier-Stokes equations to assess liquidity and systemic risk.
problem Traditional models fail to capture real market fluctuations and extreme events.
method Develops and validates a mathematical model based on Navier-Stokes equations, incorporating 13 macroeconomic and financial parameters.
result Model effectively describes liquidity dynamics, systemic risk, and extreme scenarios.
Generalizes pseudo-product structures with abnormal extremals.
problem Finiteness of symmetry algebras for non-degenerate pseudo-product structures.
method Modified universal prolongation of graded nilpotent Lie algebras and generalized finiteness criterion.
result Distributions with singularly transitive properties have finite-dimensional symmetries.
Cryptocurrency markets exhibit violent, synchronised drawdowns, challenging diversification claims.
problem Cryptocurrency markets' violent drawdowns challenge diversification claims.
method Dynamic conditional tail dependence analysis
result Near-complete and stable lower-tail graph, upper tail that thins over time, dissolution of token categories into a core.
New method reduces bias in learning from large action spaces using selective importance sampling.
problem Learning from large-scale recommendation systems with bandit feedback and supervised labels.
method Selective Importance Sampling (sIS) and Policy Optimization for eXtreme Models (POXM) algorithm.
result POXM method significantly outperforms existing methods in learning from bandit feedback on XMC tasks.
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain subgroups α ⊂ {1,. .. , d} of variables Xj. Under th…
Study on instability of extreme Reissner-Nordström spacetime perturbations.
problem Linear stability of gravitational and electromagnetic perturbations in extreme Reissner-Nordström spacetime.
method Extends Giorgi's framework to prove instability results for a set of gauge invariant quantities along the event horizon.
result Proves decay, non-decay, and polynomial blow-up estimates for certain quantities along the event horizon, depending on the number of derivatives.
We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change its economic welfare. After a long transient, the system self-organizes into a …
Improved forecasting of financial risk using Diffusion-Copula framework.
problem Capturing complex, asymmetric dependence structures in financial markets.
method Explicitly decouples marginal distribution learning from dependence structure using Mixture Density Networks and Classification-Diffusion Copula.
result Superior performance in forecasting systemic extremes of marginal and joint events.
Automates investor/company matching with AI, explaining decisions.
problem Matching companies and investors is hard due to limited data and need for explanations.
method Representation learning for small datasets + parameterized explanation generation.
result System performs well on matching task and explains decisions.
We define systems of pre-extremals for the energy functional of regular rheonomic Lagrange manifolds and show how they induce well-defined Hamilton orthogonal nets. Such nets have applications in the modelling of e.g. wildfire spread under time- and space-dependent conditions. The time function inherited from such a Ha…
Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure.…