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.
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.
Paper develops multivariate time series similarity and distance measures.
problem Compensating for misalignments in multivariate time series data.
method Adapted Independent and Dependent DTW strategies to seven elastic similarity and distance measures.
result Each measure achieves highest accuracy on at least one dataset, supporting their value.
Study approximates multivariate risk measures for Gaussian risks.
problem Complex approximations of multivariate risk measures for Gaussian risks.
method Derived precise approximations of marginal mean excess, marginal expected shortfall, and multivariate conditional tail expectation.
result Similar results hold for elliptical and Gaussian-like multivariate risks.
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
New multivariate risk measures improve on univariate OCE methods.
problem Improving risk assessment in multivariate settings.
method Inspired by univariate OCE, introduces convex, monotonic, cash-invariant measures.
result Numerical algorithms provide error estimates for computations.
New multivariate dependency measure using Gaussian kernel and copula.
problem Measuring dependency between multivariate distributions.
method Gaussian kernel distance to uniform copula, normalization, nonparametric estimate.
result Proposed measure satisfies desirable properties and is compared with existing measures.
Simplifies study of multivariate shortfall risk measures.
problem Complexity in studying multivariate shortfall risk measures.
method Defines shortfall risk measures through a 1-dimensional function.
result Simplifies properties of multivariate shortfall risk measures.
Paper proposes a new model for multivariate risk measures using Wasserstein barycenters.
problem Estimating robust multivariate risk measures in financial markets.
method Wasserstein barycenters of probability measures, copulas, Value at Risk models.
result The new model provides realistic VaR forecasts in both common and volatile periods.
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk m…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate di…
The paper explores time consistency for scalar multivariate risk measures in markets with transaction costs.
problem Time consistency of scalar multivariate risk measures in markets with transaction costs.
method Presented dual representations and derived an equivalent recursive formulation for multivariate scalar risk measures.
result Developed a direct notion of a 'moving scalarization' for scalar time consistency.
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, F measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives…
In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and rel…
This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distan…
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.
Paper introduces MTCM to measure multivariate tail dependence.
problem Classical TDC fails to capture non-exchangeable features of multivariate tail dependence.
method Extends bivariate tail copula measure to multivariate case.
result MTCM reveals off-diagonal stress directions and differences in extremal dependence.
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.
Develops efficient projections for multivariate probability measures.
problem Estimating causal effects and optimal weights in multivariate data.
method Tangent Wasserstein projections using generalized geodesics.
result Provides a unique solution for causal inference and optimal weights.
Paper introduces a new risk measure for multivariate residual estimation.
problem Quantifying residual estimation risk in complex financial models.
method Developed a multivariate framework for residual estimation risk, defined using various risk measures, and proposed a back-testing criterion.
result Demonstrated the effectiveness of the new measure through back-testing on retail credit portfolios.
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability α, the 100α% VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio ove…
New multivariate distribution for financial risk measurement.
problem Modeling dependent heavy-tailed risks in finance.
method Introduced a new absolutely continuous multivariate distribution with positively dependent Pareto margins.
result The new distribution is useful for describing dependent heavy-tailed risks in insurance.
Transmeter quickly measures transferability between different datasets.
problem Measuring transferability between heterogeneous multivariate datasets.
method Pre-trained source model, adversarial network, and encoder-decoder architecture.
result Transmeter provides the most accurate transferability measurement up to 10.3 times faster.
A new risk measure framework captures multivariate risk in banking.
problem Scalar risk measures fail to capture the multivariate nature of risk in banking.
method A novel multivariate risk measure framework based on the Magnitude-Propensity approach.
result The proposed framework provides a more comprehensive characterization of extreme events.
Spectral clustering identifies clusters of multivariate extremes.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random k-nearest neighbor graph. result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
Adversarial approach for optimizing multivariate performance measures in structured predictions.
problem Inconsistency between learner's objective and desired application performance.
method Adversarial training of structured predictions to optimize exact F-score or AER while matching training data properties.
result Improvement in multivariate performance measures for word alignment and named entity recognition.
New findings show Shannon information measures fail to accurately assess multivariate dependencies.
problem Accurately measuring information flow in complex systems.
method Demonstrated that Shannon information measures fail to distinguish between dyadic and polyadic relationships.
result Shannon information measures are inadequate for discovering meaningful dependency structures in joint probability distributions.
The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.
problem Risk management of regulation and investment purposes.
method Proposes MRVaR and MRCov as risk measures for elliptical and log-elliptical distributions.
result Explicit expressions of MRVaR and MRCov derived for multivariate (log-)elliptical distributions.
New method quantifies multivariate redundancy using maximum entropy decompositions.
problem Elusive multivariate measures of redundancy that comply with nonnegativity and axioms.
method Maximum entropy framework, rooted tree-based decompositions of mutual information.
result Quantifies different multivariate redundancy contributions.
Study proposes a new portfolio selection method using non-Gaussian models and Esscher transform.
problem Portfolio selection with complex stock return structures and skewness, kurtosis.
method Multivariate non-Gaussian models (NTS and GH), Esscher transform for risk-neutral measure, simultaneous calibration of univariate log-returns and volatility.
result Demonstrated the effectiveness of the proposed models in fitting and selecting portfolios.
Paper presents dual representations for systemic risk measures.
problem Measuring and allocating systemic risk during financial crises.
method Develops dual representations for scalar and multivariate systemic risk measures in two frameworks.
result Results cover both aggregating after allocating and allocating after aggregation.
This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approa…
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
Researchers extend CCVaR to multivariate data using Archimedean copulas.
problem No multivariate extension for CCVaR when dependence is given by Archimedean copulas.
method Derive an almost closed-form expression for CCVaR under an Archimedean copula, examine coherence conditions, and conduct numerical experiments.
result An almost closed-form expression for CCVaR under an Archimedean copula is derived.
Paper develops a novel approach to identify clusters of features in multivariate extremes.
problem Understanding the complex structure of multivariate extremes in various fields.
method Optimization-based approach to assess the dependence structure of extremes.
result Estimating clusters of features that best capture the support of extremes.
New framework for calculating multivariate risk measures using Wishart process.
problem Quantifying multivariate risk measures in financial markets.
method Introducing a new analytical framework based on the Wishart process.
result Explicit computation of conditional tail risk measures up to two dimensions.
Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and anomaly detection. One convenient (non-parametric) characterization of extremal de…
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate settings, studies its relationship with Bayes risk and mutual information, proposes an efficient importance sampling estimator.
result UNL as a measure of dependence between group labels and variables of interest, interpretable measure of partition-covariate dependence in clustering.
New method uses diffusions to measure sample quality in multivariate targets.
problem Measuring convergence to multivariate continuous targets.
method Ito diffusions and explicit multivariate Stein factor bounds.
result Established near-linear relationship between diffusion Stein discrepancies and Wasserstein distances.
New method handles correlated and repeated measurements using smoothed multivariate square-root Lasso.
problem Handling correlated and repeated measurements with complex noise structure.
method Proposes a concomitant estimator that uses non-averaged measurements and leverages smoothing theory for optimization.
result Demonstrates practical benefits on various datasets (toy, simulated, real neuroimaging).
The paper examines MSU measure and its effectiveness in feature selection.
problem Improving feature selection in multivariate data.
method Statistical simulation of MSU under different feature conditions.
result A condition is identified that maintains MSU quality across various feature combinations.
New algorithm for estimating multivariate quantiles using stochastic optimal transport.
problem Estimating multivariate quantiles from data.
method Stochastic algorithm for entropic optimal transport in Banach spaces, using Fourier coefficients.
result Almost sure convergence of the stochastic algorithm in infinite-dimensional Banach spaces.
We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We present a simulated study regarding the estimation of the risk measure VaRp on FIEGARCH processes. We consider the distr…
Paper identifies latent factors from noisy measurements using tensor decomposition.
problem Identification of latent factors from noisy, correlated measurements.
method Tensor decomposition of third order cross moments, Kruskal theorem, Kotlarski identity, generalized Kruskal rank.
result Full distribution of latent factors and measurement errors identified without injective measurements.
Spatial blind source separation simplifies multivariate spatial prediction.
problem Predicting multivariate measurements at unobserved locations with spatial dependencies.
method Spatial blind source separation as a pre-processing tool compared to Cokriging and neural networks.
result Spatial blind source separation simplifies spatial prediction by avoiding cross-dependencies.
New measures quantify mutual dependence between multiple random vectors.
problem Measuring mutual dependence between multiple random vectors.
method Proposes three measures based on generalized distance covariance.
result Empirical and simplified empirical measures effectively test mutual independence.
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical…
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate variables, establishes key properties, interprets as dependence measure, proposes efficient estimator.
result Highlights the UNL's utility in clustering for evaluating group structure dependence on covariates.