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On representing and hedging claims for coherent risk measures
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Jacka, Saul D., Armstrong, S. P. and Berkaoui, Abdelkarem (2018) On representing and hedging claims for coherent risk measures. Journal of Convex Analysis, 26 (1). ISSN 0944-6532.
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Official URL: http://www.heldermann.de/JCA/JCA26/JCA261/jca26014...
Abstract
\def\cF{\mathcal{F}} We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\cF_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\cF_t$-measurable. Hence we obtain a generalisation of F. Delbaen's m-stability condition [{\it The structure of m-stable sets and in particular of the set of risk neutral measures}, in: In Memoriam Paul-Andr{\'e} Meyer, Springer, Berlin et al. (2006) 215--258] for the problem of reserving in a collection of num\'eraires {\bf V}, called {\bf V}-m-stability, provided these cones arise from acceptance sets of a dynamic coherent measure of risk [see P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath: {\it Thinking coherently}, Risk 10 (1997) 68--71; {\it Coherent measures of risk}, Math. Finance 9(3) (1999) 203--228]. We also prove that {\bf V}-m-stability is equivalent to time-consistency when reserving in portfolios of {\bf V}, which is of particular interest to insurers.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Journal of Convex Analysis | ||||
Publisher: | Heldermann Verlag | ||||
ISSN: | 0944-6532 | ||||
Official Date: | 17 February 2018 | ||||
Dates: |
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Volume: | 26 | ||||
Number: | 1 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 19 February 2018 |
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