Jacka, Saul D. and Berkaoui, Abdelkarem (2007) On representing claims for coherent risk measures. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by introducing weak and strong versions. We then prove that the two concepts of m- stability and time-consistency are still equivalent, thus giving necessary and sufficient conditions for a coherent risk measure to be represented by a market with proportional transaction costs. We go on to deduce that, under a separability assumption, any coherent risk measure is strongly time-consistent with respect to a suitably chosen countable portfolio, and show the converse: that any market with proportional transaction costs is equivalent to a market priced by a coherent risk measure, essentially establishing the equivalence of the two concepts.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Risk -- Mathematical models
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2007
Volume:	Vol.2007
Number:	No.20
Number of Pages:	47
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Institute of Actuaries (Great Britain) (IoA)
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URI:	http://wrap.warwick.ac.uk/id/eprint/35547

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