arXiv research

The paper explores time consistency for scalar multivariate risk measures in markets with transaction costs.

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

A new risk measure framework captures multivariate risk in banking.

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…

The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can…

The paper defines and analyzes scalar risk measures in markets with transaction costs.

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…

Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Sc…

This work extends set-valued risk measures to discrete time, using difference inclusions and equations.

We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson's algorithm to solve this problem. Using Lagrangian duality, we develop sc…

Simplifies study of multivariate shortfall risk measures.

New multivariate risk measures improve on univariate OCE methods.

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

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…

The paper addresses time inconsistency in mean-risk optimization.

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…

Paper introduces a new risk measure for multivariate residual estimation.

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 MRVaR and MRCov for elliptical and log-elliptical distributions.

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

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 framework for calculating multivariate risk measures using Wishart process.

Researchers extend CCVaR to multivariate data using Archimedean copulas.

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…

Paper introduces contribution measures for systemic risk in crypto markets.

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…

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…

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 …

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

The paper bounds solutions to complex optimization problems with uncertain data.

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

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

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 concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time consistency of scalar risk measu…

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

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the exchange rules in the a…

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…

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…

The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each time and state is c…

Study systemic risk measures and capital allocation rules, showing commonalities.

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

A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a multivariate Pareto distribution. Insurance: Mathematics and Economics 46(2), 308-31…

Unified asymptotic treatment for VaR- and expectile-based systemic risk measures.

Generalizes underlap coefficient for multivariate group separation.

New set-valued star-shaped risk measures introduced for better risk assessment.

Investigates diversification quotient based on VaR and ES for portfolio models.

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