Multivariate risk measures : a constructive approach based on selections

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dc.contributor.author Cascos, Ignacio
dc.contributor.author Molchanov, Ilya
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2013-02-12T15:32:24Z
dc.date.available 2013-02-12T15:32:24Z
dc.date.issued 2013-01
dc.identifier.uri http://hdl.handle.net/10016/16112
dc.description.abstract 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 argument of the risk and so consider risk measures of set-valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set-valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. The definition of the selection risk measure is based on calling a set-valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained risk measure is coherent (or convex), law invariant and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set-valued risk measures considered by Kulikov (2008), Hamel and Heyde (2010), and Hamel et al. (2013)
dc.description.sponsorship Supported by the Spanish Ministry of Science and Innovation Grants No. MTM20II—22993 and ECO20ll-25706. Supported by the Chair of Excellence Programme of the Universidad Carlos III de Madrid and Banco Santander and the Swiss National Foundation Grant No. 200021-137527
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso eng
dc.relation.ispartofseries UC3M Working papers. Statistics and Econometrics
dc.relation.ispartofseries 13-01
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.title Multivariate risk measures : a constructive approach based on selections
dc.type workingPaper
dc.subject.eciencia Estadística
dc.rights.accessRights openAccess
dc.type.version submitedVersion
dc.identifier.repec ws130101
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