This paper studies asymptotic multivariate expectiles in risk measures.
problem Understanding the asymptotic behavior of multivariate expectiles in risk measures.
method Investigates asymptotic multivariate expectiles in a multivariate regular variations context, proposing estimators for specific tail conditions.
result Proposes estimators for multivariate asymptotic expectiles under various tail conditions.
Geometric expectiles generalize expectiles for multivariate data.
problem Generalizing expectiles for multivariate distributions.
method Convex risk minimization problem solution for d-dimensional vectors.
result Geometric expectiles are consistent risk measures under common transformations.
New DQ based on expectiles improves portfolio diversification.
problem Improving diversification in financial portfolios.
method Diversification quotient based on expectiles, offering simple formulas and pseudo-convexity.
result The expectile-based DQ is efficient and effective in portfolio optimization.
Unified asymptotic treatment for VaR- and expectile-based systemic risk measures.
problem Analyzing systemic risk measures under extreme system-wide disasters.
method Classified systemic risk measures into VaR- and expectile-based families, introduced new ICE and SICE measures, and provided second-order asymptotic results.
result Second-order asymptotics provide more accurate tail approximations for systemic risk measures.
Proposes a new clustering method based on expectiles for non-spherical clusters.
problem Inability of K-means to handle non-spherical clusters. method Uses expectiles to define cluster centers and searches for clusters via a greedy algorithm.
result Outperforms K-means and spectral clustering on asymmetric shaped clusters. Paper proves equivalences in portfolio optimization with new risk measures.
problem Portfolio optimization with novel risk measures.
method Derive subgradients and gradients for negative expectile and omega ratio.
result Negative expectile can be used as a portfolio optimization objective.
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.
The paper examines expectile quadrangle properties in risk management.
problem Exploring the properties of expectile quadrangles in risk management.
method Rigorously examines the properties of expectile quadrangles.
result Rigorously examines the properties of expectile quadrangles.
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.
Optimizes learning rates for kernel-based expectile regression.
problem Estimating conditional expectiles efficiently.
method Support vector machine type approach using Gaussian RBF kernels.
result Learning rates are minimax optimal with a logarithmic factor.
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.
Bayesian method forecasts market risks using expectiles and expected shortfall.
problem Forecasting market risks with high precision.
method Bayesian Markov Chain Monte Carlo method with nonlinear threshold specification.
result Empirical support for the proposed models in market indices forecasting.
Expectiles were defined using a minimisation principle. They form a special class of coherent risk measures. We will describe the scenario set and we will show that there is a most severe commonotonic risk measure that is smaller than the given expectile.
The paper develops robust risk measures for uncertain loss positions.
problem Risk assessment for loss positions with uncertain distributions.
method Robust optimized certainty equivalents and generalized quantiles are proposed and analyzed.
result Robust expectiles with specific penalization functions are coherent risk measures.
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes it possible to estimate expectiles in a non-parametric framework by a support vec…
ENN method uses expectile regression for genetic data analysis of complex diseases.
problem Discover additional genetic variants contributing to complex diseases.
method Developed an expectile neural network (ENN) method integrating expectile regression and neural networks.
result ENN method outperforms existing expectile regression in discovering genetic variants predisposing to sub-populations.
New Bayesian models optimize quantiles and expectiles for stochastic functions.
problem Optimizing for quantiles and expectiles in stochastic functions.
method Proposed variational models and BO strategies for quantile and expectile regression.
result Proposed models and strategies outperform existing methods in heteroscedastic, non-Gaussian settings.
Study improves risk management for volatile markets using expectiles.
problem Limitations of traditional risk measures during market stress.
method Develops expectile-based framework for FTSE 100 index.
result Expectile-based Value-at-Risk (EVaR) outperforms traditional VaR measures.
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.
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward…
Proposes a new robust expectile regression method for high-dimensional data.
problem Heterogeneity in high-dimensional data with heteroscedastic variance or inhomogeneous covariate effects.
method Iteratively reweighted ℓ1-penalization for robust expectile regression (retire).
result Oracle convergence rate after log(log d) iterations in high-dimensional settings.
Bayesian model forecasts tail risks better than traditional methods.
problem Forecasting tail risks in financial markets.
method Realized-CARE model incorporating quantile loss function and Bayesian adaptive MCMC.
result The Realized-CARE model outperforms other models in forecasting Value-at-Risk and Expected Shortfall.
DAERNN models censored data using neural networks with data augmentation.
problem Handling censored data in expectile regression.
method Data augmentation based Expectile Regression Neural Networks (ERNNs).
result DAERNN outperforms existing censored ERNNs methods and achieves comparable predictive performance to fully observed data.
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…
This paper develops statistical models for cryptocurrency returns using hidden Markov regression and copulas.
problem Capturing the interrelationships and serial heterogeneity of cryptocurrency returns.
method Hidden Markov regression models with regime-switching copulas for quantiles and expectiles.
result Captures extreme returns and their temporal evolution through a latent Markov chain.
lCARE improves EVaR model for time-varying tail risk by localizing parameters.
problem Time-varying tail risk in financial portfolios.
method Local parametric approach to fit expectile models, optimizing interval length.
result Optimal interval lengths for tail risk capture (3-6 months) improve risk assessment.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
Develops a framework for consistent loss functions with variable transformations.
problem Lack of theoretical understanding of variable transformations in consistent loss functions.
method Formal characterizations of consistency for transformed loss functions in two cases: realization and prediction variables.
result Establishes new identifiable and elicitable functionals for complex predictive tasks.
Deep Huber QRNs predict Huber quantiles for house prices.
problem Predicting more functionals of predictive probability distributions.
method Training a DL algorithm with the Huber quantile scoring function.
result DHQRNs provide satisfactory absolute performance in house price prediction.
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…
Algorithm detects influential observations in high-dimensional data.
problem Challenges in identifying influential observations in high-dimensional datasets.
method Three-step algorithm based on expectiles and asymmetric correlations.
result Higher detection power than competing methods.
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
problem Comparing and characterizing random outcomes in risk assessment.
method Exploring the equivalence between higher order risk measures and stochastic dominance, using stochastic optimization and expectiles as examples.
result Higher order risk measures and stochastic dominance are equivalent and can be used to characterize random outcomes.
Unified framework for DRL algorithms using statistical estimation.
problem Designing and analyzing DRL algorithms in terms of return distribution statistics.
method Decompose DRL algorithms into statistical estimation and return distribution imputation.
result Improved analyses and a new algorithm (EDRL) based on expectiles.
Deep RL solves dynamic risk pricing for complex financial models.
problem Dynamic risk measures in financial derivatives pricing.
method Deterministic actor-critic deep reinforcement learning (ACRL) for time-consistent expectile risk.
result High-quality hedging policies and prices for complex financial instruments.
We introduce and compare new variability measures based on risk quantiles.
problem Comparing variability measures in risk management.
method Developed a framework for one-parameter families of inter-Expected Shortfall differences and inter-expectile differences.
result Characterized symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences.
New method for insurance valuation combining hedging and risk minimization.
problem Current insurance valuation methods do not reflect regulatory risk measures.
method Two-step hedging procedure using generalised regression.
result The method produces portfolios neutral to risk measures like VaR or expectiles.
In the present contribution we characterize law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (2006), we show that these risk measures can be identified with a class of generalized shortfall risk measures. As a direct consequence, we are …
The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible,…
Introduces generalized Orlicz premia for broader applicability.
problem Developing a flexible framework for insurance premium calculation.
method Introduces a generalized Orlicz premium definition using non-convex loss functions.
result Generalized Orlicz premia encompass various specific cases and maintain key properties.
The paper examines stochastic ordering of Gini indexes for multivariate elliptical risks.
problem Stochastic ordering of Gini indexes for multivariate elliptical risks.
method Established conditions for monotonicity of Gini index in usual stochastic order.
result Suitable conditions for multivariate elliptical risks generalize those for multivariate normal risks.
Unified approach to risk measurement using Skew Exponential Power distribution.
problem Direct measurement of market risk with improved asymmetry and non-linearity.
method Unified Bayesian Conditional Autoregressive Risk Measures using Skew Exponential Power distribution with semiparametric P-spline approximation.
result Demonstrated effectiveness on real data of five stock market indices.
PCA simplifies multivariate extreme data analysis.
problem Analyzing multivariate extreme values with high-dimensional data.
method Principal Component Analysis (PCA) for dimensionality reduction.
result PCA helps preserve essential information for extreme value analysis.
New risk measures for multivariate data, consistent and decomposable.
problem Developing consistent risk measures for multiple variables.
method Showed strong consistency leads to decomposition into aggregation and univariate risk.
result Multivariate risk measures are conditional certainty equivalents under strong consistency.
hyppo simplifies multivariate hypothesis testing in Python.
problem Inconsistent multivariate hypothesis testing interfaces in Python.
method Unified library for multivariate testing procedures.
result Easy-to-use and flexible for future extensions.
This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
RED CoMETS improves multivariate time series classification accuracy.
problem Complexity of multivariate time series classification.
method Ensemble classifier RED CoMETS for symbolically represented multivariate time series.
result RED CoMETS achieves highest reported accuracy on 'HandMovementDirection' dataset.
We study various specializations of the colored HOMFLY-PT polynomial. These specializations are used to show that the multivariable link invariants arising from a complex family of sl(m|n) super-modules previously defined by the authors contains both the multivariable Alexander polynomial and Kashaev's invariants. We c…
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.