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) 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, 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: | Date Event 2007 Published |
| Volume: | Vol.2007 |
| Number: | No.20 |
| Number of Pages: | 47 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Open Access (Creative Commons open licence) |
| 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) |
| URI: | https://wrap.warwick.ac.uk/35547/ |
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