  We show how risk measures originally defined in a model free framework in
terms of acceptance sets and reference assets imply a meaningful underlying
probability structure. Hereafter we construct a maximal domain of definition of
the risk measure respecting the underlying ambiguity profile. We particularly
emphasise liquidity effects and discuss the correspondence between properties
of the risk measure and the structure of this domain as well as
subdifferentiability properties.
  Keywords: Model free risk assessment, extension of risk measures, continuity
properties of risk measures, subgradients.
