Some classes of multivariate risk measures

Cardin, Marta; Pagani, Elisa

doi:10.1007/978-88-470-1481-7_7

Cited by 4 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The remainder of this section is devoted to providing some properties of V aR u α (X) which are similar to those properties considered in the risk literature; (see [Artzner et al (1999), Burgert and Ruschendorf (2006), Cardin and Pagani (2010), Rachev et al (2008), Cascos and Molchanov (2007), Cascos and Molchanov (2013)]). Specifically, we provide properties of the multivariate V aR u α (X) in terms of the [Artzner et al (1999)]'s properties related to coherent risk measures in the univariate setting.…”

Section: Directional Multivariate Value At Riskmentioning

confidence: 98%

“…We are aware that this procedures can be improved using more sophisticated tools of the non-parametric statistics, but they are material for another project. On the other hand, it is well known that in risk theory, it is desirable that a measure be robust, (see [Artzner et al (1999), Burgert and Ruschendorf (2006), Cardin and Pagani (2010), Rachev et al (2008)]). But in general, most of the measures are sensitive to atypical observations.…”

Section: Robustnessmentioning

confidence: 99%

See 1 more Smart Citation

A directional multivariate value at risk

Torres

Lillo

Laniado

2015

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

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 over the given time horizon exceeds this value is α. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in R n , or to a property of the univariate quantile that is desirable to be extended to R n . In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate VaR over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.

show abstract

Section: Directional Multivariate Value At Riskmentioning

confidence: 98%

Section: Robustnessmentioning

confidence: 99%

A directional multivariate value at risk

Torres

Lillo

Laniado

2015

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

show abstract

“…The quantity C E is indeed a certainty equivalent. Moreover, the concept of equally distributed equivalent income is interpretable as a Debreu's coecient, see equation (22).…”

Section: Inequality Measuresmentioning

confidence: 99%