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.
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.
The paper estimates CoVaR with various models for financial risk analysis.
problem Estimating conditional value-at-risk with financial time series data.
method Fitting multivariate parametric models and copula functions to capture stylized facts of equity returns.
result Backtesting shows that certain models provide better risk estimates than others.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
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.
Optimizes cryptocurrency portfolios using MNTS GARCH model.
problem Optimizing cryptocurrency portfolios with non-Gaussian return dynamics.
method Multivariate normal tempered stable (MNTS) GARCH model for non-Gaussian returns, Foster-Hart risk optimization.
result Foster-Hart optimization yields a more profitable portfolio with better risk-return balance.
New method allocates capital based on tail central moments for financial risk assessment.
problem Inability of CTE-based capital allocation to reflect tail behavior of losses.
method Developed TCM-based capital allocation for normal mean-variance mixture distributions.
result TCM-based method captures tail risk contributions not detected by CTE.
GPDFlow models extreme threshold exceedance with flexible dependence using normalizing flows.
problem Challenges in modeling multivariate threshold exceedance probabilities due to infinite parametrizations.
method GPDFlow uses normalizing flows to flexibly represent dependence without explicit parametric assumptions.
result GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.
Proposes a new portfolio optimization method considering reward, dispersion, and asymmetry.
problem Capturing fat-tails and asymmetry in asset return distributions.
method Market model with tempered stable distribution; extended mean-variance optimization.
result Closed-form solutions for VaR and CVaR; efficient frontier extended to three dimensions.
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…
The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.
problem Mitigating left tail risk in multi-asset portfolios.
method Proposes a Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) for portfolio optimization.
result Optimal portfolios with tail risk measures outperform standard deviation-based portfolios and equally weighted portfolios in various performance metrics.
Unified econometric model for portfolio optimization and option valuation.
problem Time-varying volatility and heavy tails in asset returns.
method Multivariate affine GARCH(1,1) with Normal Inverse Gaussian innovations.
result Substantial wealth-equivalent utility losses from ignoring correlation and tail risk.
In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multiv…
We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the d…
This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance …
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
A two-step nonparametric method estimates financial systemic risk.
problem Estimating CoVaR due to unobservability of multivariate-quantiles.
method Two-step nonparametric approach using Monte-Carlo simulation and kernel method.
result Consistency and asymptotic normality of the two-step estimator established.
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.
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…
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.
This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default under multi-factor models. Due to the amount of the portfolio, the heterogeneous effect of obligors, and the phenomena that default events are rare and mutually dependent, it is…
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.
New method for geodesics of multivariate normals, derived from a Toda lattice.
problem Computing geodesics of multivariate normal distributions.
method Using block Cholesky decomposition and a natural Riemannian submersion, a new Toda lattice type Lax pair is derived.
result A new Toda lattice type Lax pair derived from geodesics and block Cholesky decomposition.
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…
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
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.
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…
Study uses copulas and DCC-GARCH for multivariate risk analysis of VaR and CVaR.
problem Multivariate risk analysis for Value at Risk (VaR) and Conditional Value at Risk (CoVaR).
method Copulas and Dynamic Conditional Correlation (DCC)-GARCH models applied to historical financial data.
result Comparison of different copula families for goodness-of-fit and effectiveness.
AGCA approximates angular variation on the unit sphere, reducing extremal dependence problems to eigenanalysis.
problem Approximating angular variation in multivariate extremes.
method Anchored geodesic component analysis (AGCA) approximates angular variation by great subspheres constrained to pass through a chosen reference direction.
result AGCA finds concentrated tail directions in daily equity-portfolio losses, explaining about 91% of anchored variation.
A novel model combines deep learning and extreme value theory for multivariate cyber risk prediction.
problem High dimensionality and heavy tails in multivariate cyber risk patterns.
method Combines deep learning for point predictions and extreme value theory for quantile predictions.
result The model provides satisfactory high quantile predictions and accurate point predictions.
Characterizes connections on multivariate normal distributions.
problem Characterizing connections on statistical manifold of multivariate normal distributions.
method Analyzes statistical manifold (N,gF,ablaA,ablaA∗) of multivariate normal distributions. result The Amari-Chentsov connection ablaA is characterized by conjugate symmetry. 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.
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various multivariate risk measures significantly. In this contribution we derive precise approxim…
A new algorithm speeds up elliptical slice sampling for truncated multivariate normals.
problem Efficiently sampling from truncated multivariate normal distributions with linear constraints.
method Adapting elliptical slice sampling to linearly truncated multivariate normals, with an algorithm for ellipse-polytope intersection in O(m log m) time.
result The algorithm enhances numerical stability, speeds up running time, and is easy to parallelize.
Enhances normal mean estimation with side info using NIT approach.
problem Compound estimation of normal means with side information.
method Empirical Bayes, nonparametric integrative Tweedie (NIT) approach.
result NIT approach improves estimation risk and convergence rate with increasing auxiliary data.
The paper introduces a new class of multivariate mixtures for actuarial applications.
problem Developing a new class of multivariate mixtures for actuarial calculations.
method Proposed a class of multivariate matrix-exponential affine mixtures with matrix-exponential marginals.
result Explicit calculations of actuarial quantities are possible due to the proposed class's properties.
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 distances for comparing multivariate normal distributions.
problem Comparing multivariate normal distributions efficiently and accurately.
method Approximated Fisher-Rao distance and pullback SPD cone distances.
result Efficient computation of distances between normal distributions.
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
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.
Extends SORTE to multivariate risk functions.
problem Analyzing systemic risk in financial institutions or insurance-reinsurance markets.
method Develops a new framework for multivariate utility functions and applies duality theory.
result Proves existence, uniqueness, and Nash Equilibrium property of Multivariate Systemic Optimal Risk Transfer Equilibrium.
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.
The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted variance-covariance matrices. The objective is to show how to generate datasets for a kn…
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.
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.
This paper improves credit risk analysis by incorporating state-dependent recovery rates into a factor model.
problem Accurate default forecasting in credit risk analysis.
method Extends a one-factor Gaussian copula model to include state-dependent recovery rates and a common factor.
result The proposed model outperforms other models in default prediction, especially during hectic periods.