Bayesian method models normal and anomalous behaviors using extreme value theory.
problem Challenges in setting optimal thresholds for anomaly detection.
method Probabilistic framework using Dirichlet Process Mixture Model and extreme value theory.
result Explicit modeling of normal and anomalous behaviors leads to robust anomaly detection.
The study examines the asymptotic behavior of extremal length in Teichmüller space.
problem Understanding the asymptotic behavior of extremal length along Teichmüller rays.
method Analyzing the limit of extremal length and deriving formulas for limiting Teichmüller distance and detour metric.
result An explicit formula for the limiting Teichmüller distance and a necessary and sufficient condition for Teichmüller rays to be asymptotic.
Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp Lq regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of Rn, which imply asymptotic behavior of the solutions at i…
Extends extreme value mixture models to identify changepoints in financial extreme regimes.
problem Inference over financial extreme regimes is affected by threshold choice.
method Extends extreme value mixture models to account for distributional extreme changepoints using MCMC algorithms.
result Inclusion of different extreme regimes improves financial applications compared to static and dynamic approaches.
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.
Detects changes in signal covariance matrix using extreme eigenvalues.
problem Detects abrupt changes in signal covariance matrix from identity to low-rank.
method Sequential detection based on extreme eigenvalues of sample covariance matrix.
result Effective detection of behavior changes in swarm data.
Robinhood users react strongly to overnight price changes and big losers, trading quickly after extreme losses.
problem Understanding trading behavior of Robinhood users, especially in high-frequency trading scenarios.
method Analyzed intraday and overnight price changes, focusing on big losers and gainers.
result Robinhood users react more to overnight price changes and big losers, trading quickly after extreme losses.
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calcula…
We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information ab…
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…
We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle 9pi - theta, for a suitable theta with cos(theta) in Q(sqrt{19}). Relying on some delicate capacity estimates, we also show that the extrem…
Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as the extreme instance of financial bubbles and crashes, imply that markets (at lea…
Study improves L∞ estimates and extreme value behavior in stochastic differential games.
problem Analyzing the mean-field limit of diffusive games through master equation.
method Using the Master Equation to approximate state processes and establishing L∞ estimates for the total error. result Established No∞ asymptotic behavior of upper order statistics of Nash states, initiating Extreme Value Theory for stochastic differential games. Paper evaluates CRPS for extreme event forecasts, finding it unsuitable.
problem Verifying probabilistic forecasts of extreme events is challenging.
method Formal framework using extreme value theory to assess CRPS as a random variable.
result CRPS is unsuitable for extreme event verification.
Study on extremizers for Sobolev inequality on curved manifolds.
problem Existence of extremizers for the sharp p-Sobolev inequality on Riemannian manifolds with nonnegative curvature. method Nonsmooth concentration compactness methods and Mosco-convergence results for Cheeger energy.
result Almost extremal functions are close to radial Euclidean bubbles and almost zero globally under nonnegative curvature.
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evide…
The paper studies knot Floer homology under Murasugi sum and establishes graded isomorphisms.
problem Behavior of knot Floer homology under Murasugi sum.
method Established a graded version of Ni's isomorphism and proved τ=g for each summand.
result Graded isomorphisms between extremal knot Floer homologies of Murasugi sum and tensor products.
Modeling spatial extremes with non-Gaussian fields using SAR models and CNNs.
problem Challenges in modeling spatial data with heavy-tailed distributions and missing cells.
method Spatial autoregressive models with Generalized Extreme Value innovations, combined with CNN for fast parameter estimation.
result Effective modeling of spatial extremes in non-Gaussian fields, demonstrated on precipitation data.
Extreme value theory enhances statistical learning extrapolation for rare events.
problem Challenges in traditional machine learning methods for extreme data.
method Asymptotic theory and statistical tools for tail behavior.
result Effective extrapolation methods for extreme quantiles and anomalies.
In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can be connected by a path c…
Model market shows self-organized behavior with price adjustments.
problem Understanding collective behavior in market economics.
method Simple model of market economics with extremal dynamics.
result Market self-organizes through price adjustments in critical states.
Paper proposes a risk index combining frequency and severity of abnormal driving patterns.
problem Assessing driver risk based on telematics data.
method Combines frequency of abnormal driving patterns with severity quantified through tail rarity.
result Developed a risk index that enables reliable discrimination and ranking of drivers.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, includi…
New model explains volatility after extreme stock market events.
problem Understanding volatility dynamics after extreme stock market events.
method Proposed a new dynamical model using high frequency minute data.
result Volatility after extreme events follows a stretched exponential decay initially and a power law decay later.
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.
Study compares Bitcoin and Ethereum tail behavior using Q-Q plots.
problem Examining tail risk in cryptocurrency returns.
method Used Q-Q plots and Generalized Tempered Stable (GTS) distribution.
result Ethereum shows more extreme values than Bitcoin, indicating greater tail risk.
Empirical study on UEEs reveals liquidity's role and universal recovery patterns.
problem Understanding and stabilizing financial markets affected by UEEs.
method Comparative analysis of UEEs over different years in US stock market.
result Liquidity is dominant in UEEs emergence and recovery patterns are universal.
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.
The paper studies the curvature behavior near the boundary of certain domains.
problem Investigating the asymptotic behavior of bisectional curvature for weighted Bergman metrics.
method Characterizing extremal functions via L2-orthogonal projections and using the squeezing function. result The bisectional curvature at strongly pseudoconvex boundary points asymptotically matches that of the unit ball.
Deep learning predicts energy loads and prices with LSTM and EVT.
problem Predicting extreme loads in energy grids due to supply and demand fluctuations.
method Deep spatio-temporal models and EVT for tail behavior of load spikes.
result Deep LSTM models outperform traditional methods in capturing nonlinearities.
Study analyzes player churn and purchasing behavior in games.
problem Retaining players and predicting churn in video games.
method Deep behavioral analysis and ensemble learning models.
result Discarding certain churners improves prediction models.
Efficiently estimates GEV distribution parameters using neural networks.
problem Computational intensity of maximum likelihood estimation for GEV distribution.
method Neural network-based likelihood-free estimation method.
result Comparable accuracy to maximum likelihood method with significant speedup.
The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.
problem Behavioral distortions in probability weighting affect portfolio optimization under different return distributions.
method Developed a unified framework to extract probability weighting functions from optimal portfolios modeled under Gaussian and NIG distributions.
result Increasing tail fatness amplifies behavioral distortions, and shifts in risk-free rates alter the curvature of these distortions.
We assess cluster stability by trimming extreme points and tracking data range reduction.
problem Assessing stability of one-dimensional clusters.
method Probabilistic method using diameter-shrinkage ratio to track data range reduction.
result Our method achieves higher accuracy than classical tests in small or noisy samples.
A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; (ii) computation of the local volatility based on the resulting call…
Paper analyzes privacy-aware mobility behavior using entropy metrics.
problem Intrusive user location tracking makes it easy to identify users.
method Proposes spatio-temporal entropy to quantify mobility, uses GAMs to study effects of variables.
result Global GAM provides more accurate predictions of spatio-temporal entropy.
The majority of real-world networks are dynamic and extremely large (e.g., Internet Traffic, Twitter, Facebook, ...). To understand the structural behavior of nodes in these large dynamic networks, it may be necessary to model the dynamics of behavioral roles representing the main connectivity patterns over time. In th…
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
problem Investigates the behavior of Value-at-Risk (VaR) for sums of one-sided random variables.
method Analyzes the extremal aggregation behavior of VaR, introduces structural conditions for super-additivity.
result Characterizes when VaR is fully super-additive and provides unified framework for various dependence structures.
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…
Projective embedding study for surfaces with cusp singularities.
problem Understanding stability of extremal Kähler metrics on surfaces with singularities.
method Analyzing Bergman kernel behavior in three regions, focusing on the neck region.
result L^2 projective embedding asymptotically almost balanced for surfaces with cusp singularities.
The paper examines the stability of two spherical self-similar solutions in Minkowski spacetime.
problem Stability of timelike extremal hypersurfaces in Minkowski spacetime.
method Analysis of linear and nonlinear stability, construction of Newton's polygon.
result Explicit lightlike self-similar solutions are nonlinearly stable inside a subset of the backward lightcone.
The paper analyzes how tail risks and extreme volatility affect stock prices across different investment horizons.
problem Investment risk and its pricing across various horizons.
method Proposes a quantile spectral beta representation to decompose covariance and identify risk.
result Tail risk is short-term, while extreme volatility risk is long-term, affecting different asset classes.
Behavior modification improves prediction accuracy by nudging user behavior.
problem Improving prediction accuracy using behavior modification techniques.
method Combining prediction and behavior modification with reinforcement learning algorithms.
result Behavior modification can make predictions more certain but may not generalize.
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few year…
Paper proves long-term investor behavior based on power utility coefficient.
problem Understanding long-term behavior of optimal strategies in financial markets.
method Bayesian financial market model with power utility maximization.
result Optimal strategy behavior depends on power utility coefficient sign.
Approach predicts extubation readiness with high accuracy.
problem High reintubation rates due to inconsistent extubation readiness prediction.
method Random Forest classifiers trained on undersampled cardiorespiratory variability data.
result 71% of infants who failed extubation were correctly identified.