Extends sublinear expectations to random sets, identifying extremal and constructing methods.
problem Extending sublinear expectations to random sets.
method Identifying extremal expectations and presenting general construction methods.
result Identification of extremal sublinear and superlinear expectations.
The paper calculates VaR and CTE for extreme and aggregate risks using FGM copula.
problem Estimating risk measures for extreme and aggregate risks of dependent and independent markets.
method Used FGM copula to model dependence, exponential and pareto distributions for marginal risks.
result Effect of dependency on VaR and CTE of extreme and aggregate risks analyzed.
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…
This paper is a survey of some recent progress on the study of Calabi's extremal Kähler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then tu…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a hea…
Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
The paper calculates extreme measures in continuous time conic finance.
problem Determining valuation bounds for financial claims.
method Using dynamic spectral risk measures and estimating extreme measures from market data.
result Explicit formulas for extreme measures' Radon-Nykodim derivatives and estimation methods.
New bandit algorithms focus on extreme values, outperforming existing methods.
problem Optimizing decisions based on extreme values rather than expected values.
method Robust statistics-based algorithms with vanishing extremal regret.
result The proposed algorithms achieve superior performance compared to existing methods.
Quantum algorithm for dynamic asset allocation using expected shortfall.
problem Dynamic risk management in finance, especially tail risks.
method Quantum annealing algorithm in QUBO form for expected shortfall constraint.
result Quantum algorithm provides a faster solution for dynamic asset allocation.
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.
New approach simplifies proof of wave equations on black holes.
problem Global existence and decay for semilinear wave equations on extremal Reissner-Nordström black holes.
method Develops a new approach based on weaker estimates, avoiding near-horizon sharp estimates.
result Simpler and more streamlined proof without requiring near-horizon sharp estimates.
Combines VaR and ES forecasts for cryptocurrency market risk management.
problem Improving tail risk forecasts in financial markets.
method Proposes semiparametric and parametric combination frameworks.
result Combined forecasts outperform individual VaR and ES forecasts.
We propose an extension of the concept of Expected Improvement criterion commonly used in Kriging based optimization. We extend it for more complex Kriging models, e.g. models using derivatives. The target field of application are CFD problems, where objective function are extremely expensive to evaluate, but the theor…
The hidden tail of empirical distributions is analyzed using extreme value theory.
problem Understanding the bias between in-sample mean and true statistical mean for large n. method Extreme value theory applied to empirical distributions and their moments.
result The hidden moment of order 0 for power law distributions follows an exponential distribution with expectation 1/n. Risk is an inherent feature of agricultural production and marketing and accurate measurement of it helps inform more efficient use of resources. This paper examines three tail quantile-based risk measures applied to the estimation of extreme agricultural financial risk for corn and soybean production in the US: Value …
Proposes a network-based strategy to manage financial market risks.
problem Managing extreme events in volatile financial markets.
method Extreme value theory, network model, maximum independent set, value at risk, expected shortfall.
result Developed portfolio strategies improve risk diversification.
Reply to Tetlock et al. on tail risk and probability gap.
problem Expert judgment fails to account for tail risk.
method Comparison of forecasting tournaments and extreme value theory.
result Greater gap between tail expectation and probability properties.
Develops a climate risk model for asset managers.
problem Climate-related risks affecting asset performance and productivity.
method Uses the Vasicek model with downward jumps to represent climate impacts on asset dynamics.
result Expected losses increase over time due to climate-related extreme events.
Dual representation and properties of expectile-based expected shortfall studied.
problem Studying the expectile-based expected shortfall as a risk measure.
method Provided dual representation in terms of Bochner integral, showed boundedness properties, and computed for selected distributions.
result Explicit dual representation and boundedness properties of expectile-based expected shortfall.
Study on expectile and expected shortfall for tail risk assessment.
problem Comparing expectile and expected shortfall for tail risk assessment.
method Duality results and optimized certainty equivalent.
result Derived bounds and asymptotic behavior of expectile with respect to expected shortfall.
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any statistical assumptions about the source of the vectors. This problem arises as…
This paper assesses tail risk and systemic risk in cryptocurrencies using expectiles and MES.
problem Quantifying tail risk and systemic risk in cryptocurrencies.
method The study uses expectiles and Marginal Expected Shortfall (MES) to assess tail risk and systemic risk of cryptocurrencies.
result The expectile-based approach and MES provide a dynamic method to evaluate the impact of single assets on systemic risk.
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…
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.
The main aim of this paper is to inspect the properties of survey based on households inflation expectations, conducted by Reserve Bank of India. It is theorized that the respondents answers are exaggerated by extreme response bias. Latent class analysis has been hailed as a promising technique for studying measurement…
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.
We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating t…
By the Riemann-mapping theorem, one can bijectively map the interior of an n-gon P to that of another n-gon Q conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of P to those Q. In this case, one wants to find the ``best" mapping between these polygons, i.e.…
Recent financial disasters have emphasised the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme events strongly relies on their flexibility to account for the highly nonlinear and a…
Study finds sales forecasters overreact to extreme news.
problem Understanding how forecasters react to sales growth news.
method Proposes a framework with fat-tailed dynamics and linear forecasting rule.
result Forecasters overreact to significant sales growth news.
Constructs optimal symplectic connections for Kaehler metrics on holomorphic submersions.
problem Finding canonical relatively Kaehler metrics on holomorphic submersions.
method Extremal Kaehler metrics, optimal symplectic connections, and adiabatic classes.
result Constructs Kaehler metrics with constant scalar curvature and extremal metrics.
We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sampl…
Improved Hawkes model forecasts extreme financial returns more accurately.
problem Forecasting extreme tail events in financial log-returns.
method 2T-POT Hawkes model with multiple exceedance thresholds.
result 2T-POT Hawkes model outperforms GARCH-EVT model in risk forecasting.
An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having …
This paper improves uncertainty quantification in ELM models.
problem Uncertainty in ELM predictions due to data assumptions and randomness.
method Analytical derivations and variance estimates under various conditions.
result Improved understanding and estimation of ELM variability.
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be co…
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. Smooth Contextual Bandits bridge two previously studied extremes of non-differentiable and parametric-response bandits.
problem Nonparametric contextual bandits with Hölder smoothness.
method Developed a novel algorithm that optimally balances between non-differentiable and parametric-response bandits.
result Proved the algorithm achieves rate-optimal regret for all smoothness settings.
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic re…
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.
This paper presents a novel scaling method for unbiased risk estimation.
problem Challenges in risk assessment due to limited data, non-stationarity, and heavy tails.
method Develops a statistical framework for efficient risk scaling, extending beyond the square-root-of-time rule.
result Ensures robust and conservative risk estimation, applicable to small sample settings.
The paper introduces a new method for forecasting financial risk using quantile-based modeling.
problem Forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) for financial returns.
method Semiparametric approach using restricted quantile regression to model the conditional scale of financial returns.
result The method provides robust, distribution-free estimates of extreme losses and captures risk dynamics.
Study identifies key drivers and spatio-temporal trends of extreme Mediterranean wildfires.
problem Understanding and predicting the impacts of climate change on wildfire activity.
method Statistical deep-learning model combining meteorological, land cover, and orographic data.
result Vapour-pressure deficit significantly affects wildfire occurrence, while air temperature and drought affect spread.
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.
Develops a model for analyzing cryptocurrency returns focusing on extreme values.
problem Analyzing extreme returns in cryptocurrency time series.
method Linear expectile hidden Markov model with time-dependent coefficients.
result The method effectively captures the temporal evolution of extreme returns.
Throwing away data can improve worst-group error in imbalanced datasets.
problem Improving worst-group accuracy in imbalanced datasets.
method Leveraging extreme value theory to analyze the tails of data distributions and their impact on classifier performance.
result Throwing away data restores geometric symmetry in classifiers, improving worst-group generalization.
The study investigates the consistency of k-means clustering under finite expectation assumptions.
problem Consistency of k-means clustering under finite expectation assumptions. method Investigates the conditions under which k-means clustering is consistent, considering finite expectation instead of finite variance. result Inconsistency can arise due to extreme cluster imbalance, leading to some clusters having few points.