RT Generic
T1 Multivariate risk measures : a constructive approach based on selections
A1 Cascos Fernández, Ignacio
A1 Molchanov, Ilya
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB Since risky positions in multivariate portfolios can be offset by various choices ofcapital requirements that depend on the exchange rules and related transaction costs, itis 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 riskand so consider risk measures of set-valued portfolios. This situation includes theclassical Kabanov's transaction costs model, where the set-valued portfolio is given bythe sum of a random vector and an exchange cone, but also a number of further cases ofadditional liquidity constraints.The definition of the selection risk measure is based on calling a set-valued portfolioacceptable if it possesses a selection with all individually acceptable marginals. Theobtained risk measure is coherent (or convex), law invariant and has values being upperconvex closed sets. We describe the dual representation of the selection risk measureand suggest efficient ways of approximating it from below and from above. In case ofKabanov's exchange cone model, it is shown how the selection risk measure relates tothe set-valued risk measures considered by Kulikov (2008), Hamel and Heyde (2010),and Hamel et al. (2013)
YR 2013
FD 2013-01
LK https://hdl.handle.net/10016/16112
UL https://hdl.handle.net/10016/16112
LA eng
NO 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 BancoSantander and the Swiss National Foundation Grant No. 200021-137527
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RD 29 jun. 2024