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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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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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) | ||||
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Dates: |
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Volume: | Vol.2007 | ||||
Number: | No.20 | ||||
Number of Pages: | 47 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Institute of Actuaries (Great Britain) (IoA) |
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