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On representing claims for coherent risk measures
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Jacka, Saul D. and Berkaoui, Abdelkarem (2007) On representing claims for coherent risk measures. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2007 (No.20).

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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) timeconsistency with
respect to a portfolio of assets, generalizing the one defined in Delbaen [7].
In a similar way we extend the notion of mstability, by introducing weak and strong
versions. We then prove that the two concepts of m stability and timeconsistency
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
timeconsistent 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 
Official 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Status:  Not Peer Reviewed 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) 
References:  [1] Artzner, Delbaen, Eber and Heath (1999): Coherent measures of risk. Math. Finance 9 no. 3, 
URI:  http://wrap.warwick.ac.uk/id/eprint/35547 
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