Multivariate extensions of expectiles risk measures

On multivariate extensions of Value-at-Risk

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 distribution functions whereas the upper-orthant VaR is constructed from level ...

Relationship between multivariate concordance and risk measures

The question about the definition of concordance between random vectors is an open problem because there is not an unanimous opinion about its meaning and its appropriate definition. Also the definition of multivariate risk measures encounters many difficulties. In this paper we want to investigate the relationship between these multivariate measures, essentially based on the relation between r...

Multivariate extensions of McNemar's test.

This article considers global tests of differences between paired vectors of binomial probabilities, based on data from two dependent multivariate binary samples. Difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution. For detecting the first type of difference, we propose a multivariate extension of McNemar's test and show that it ...

Properties and calculation of multivariate risk measures: MVaR and MCVaR

A recent paper by Prékopa (2012) presented results in connection with Multivariate Value-at-Risk (MVaR) that has been known for some time under the name of p-quantile or p-Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value-at-Risk (MCVaR). The purpose of this paper is to further develop the theory and methodology of MVaR and MCVaR....

Estimating Value at Risk and Expected Shortfall Using Expectiles