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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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
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:	Date Event 17 February 2018 Accepted
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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