  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.
