Multivariate risks and depth-trimmed regions

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dc.contributor.author Cascos, Ignacio
dc.contributor.author Molchanov, Ilya
dc.date.accessioned 2006-11-09T10:59:42Z
dc.date.available 2006-11-09T10:59:42Z
dc.date.issued 2006-06
dc.identifier.uri http://hdl.handle.net/10016/246
dc.description.abstract 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.format.extent 415517 bytes
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.ispartofseries UC3M Working Papers. Statistics and Econometrics
dc.relation.ispartofseries 2006-15
dc.title Multivariate risks and depth-trimmed regions
dc.type workingPaper
dc.subject.eciencia Estadística
dc.rights.accessRights openAccess
dc.identifier.repec ws063815
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