On representing and hedging claims for coherent risk measures

Saul Jacka; Seb Armstrong; Abdelkarem Berkaoui

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arXiv · 1703.03638

On representing and hedging claims for coherent risk measures

Saul Jacka·Seb Armstrong·Abdelkarem Berkaoui

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Abstract

We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\mathcal{F}_t$-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition for the problem of reserving in a collection of num\'eraires $\mathbf{V}$, called $\mathbf{V}$-m-stability, provided these cones arise from acceptance sets of a dynamic coherent measure of risk. We also prove that $\mathbf{V}$-m-stability is equivalent to time-consistency when reserving in portfolios of $\mathbf{V}$, which is of particular interest to insurers.

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BibTeX RIS

Saul Jacka, Seb Armstrong, Abdelkarem Berkaoui. 2017-03-10. On representing and hedging claims for coherent risk measures. https://arxiv.org/abs/1703.03638

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