Multivariate risks and depth-trimmed regions
| dc.creator | Cascos, Ignacio | |
| dc.creator | Molchanov, Ilya | |
| dc.date | 2006-06-21 | |
| dc.date | 2006-11-20 | |
| dc.date.accessioned | 2026-07-07T12:07:19Z | |
| dc.date.available | 2026-07-07T12:07:19Z | |
| dc.description | 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 measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship. | |
| dc.description | 26 pages. Substantially revised version with a number of new results added | |
| dc.identifier | https://arxiv.org/abs/math/0606520 | |
| dc.identifier | http://arxiv.org/abs/math/0606520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208929 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | Risk Management | |
| dc.subject | 91B30; 91B82; 60D05; 62H99 | |
| dc.title | Multivariate risks and depth-trimmed regions | |
| dc.type | text |