  The paper considers trading with proportional transaction costs. We give a
necessary and sufficient condition for A, the cone of claims attainable from
zero endowment, to be closed, and show, in general, how to represent its
closure in such a way that it is the cone of claims attainable for zero
endowment, for a different set of trading prices. The new representation obeys
the Fundamental Theorem of Asset Pricing. We then show how to represent claims
and in a final section show how any such setup corresponds to a coherent risk
measure.
