arXiv research

Paper proposes a new method to evaluate joint risk under uncertainty.

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the m…

Simplifies study of multivariate shortfall risk measures.

This paper uses multivariate probability models to assess financial system risks.

Paper proposes a new model for multivariate risk measures using Wasserstein barycenters.

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.

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.

A novel model combines deep learning and extreme value theory for multivariate cyber risk prediction.

Researchers extend CCVaR to multivariate data using Archimedean copulas.

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…

The paper introduces a new class of multivariate mixtures for actuarial applications.

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…

Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.

The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.

Extended univariate Range Value-at-Risk to multivariate settings.

A new risk measure framework captures multivariate risk in banking.

The paper estimates CoVaR with various models for financial risk analysis.

Paper introduces a new risk measure for multivariate residual estimation.

The paper calculates moments and conditional risks for skewed elliptical distributions.

In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive form…

Optimizes dynamic investment portfolios with correlated jumps.

Forecast reconciliation improves portfolio risk forecasts, especially when true covariance is known.

Enhanced multivariate GARCH model using LSTM for better volatility forecasting.

New framework for calculating multivariate risk measures using Wishart process.

A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample v…

New methods estimate multivariate shortfall risk more efficiently.

Paper introduces MSPD for multivariate risk processes with dependencies.

We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for the study of the dyna…

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a …

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…

Unified econometric model for portfolio optimization and option valuation.

In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for discrete probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions given for continuous random variables when adapt…

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 $VaR_p$ on FIEGARCH processes. We consider the distr…

In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk meas…

The book chapter discusses tail risk analysis for financial data using extreme value statistics.

This paper uses VAE to generate extreme events from multivariate data.

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different tail thickness. After a discussion of relevant estimation and …

Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…

Paper introduces contribution measures for systemic risk in crypto markets.

Sharp bounds found for various risk measures using generalized FGM copulas.

Develops a new model to better estimate cryptocurrency and stock volatility.

The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the compu…

The paper analyzes risk spillovers between AI ETFs, AI tokens, and green markets.

The paper examines how heavy-tailed risks behave under Gaussian copula models.