On representing claims for coherent risk measures
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).
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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 . 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|
|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|Status:||Not Peer Reviewed|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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