  Risk measures, or coherent measures of risk are often considered on the space
L^\infty, and important theorems on risk measures build on that space. Other
risk measures, among them the most important risk measure---the Average
Value-at-Risk---are well defined on the larger space L^1 and this seems to be
the natural domain space for this risk measure. Spectral risk measures
constitute a further class of risk measures of central importance, and they are
often considered on some L^p space. But in many situations this is possibly
unnatural, because any L^p with p>p_0, say, is suitable to define the spectral
risk measure as well. In addition to that risk measures have also been
considered on Orlicz and Zygmund spaces. So it remains for discussion and
clarification, what the natural domain to consider a risk measure is? Abstract
This paper introduces a norm, which is built from the risk measure, and a
Banach space, which carries the risk measure in a natural way. It is often
strictly larger than its original domain, and obeys the key property that the
risk measure is finite valued and continuous on that space in an elementary and
natural way.
