  It is shown that the axioms for coherent risk measures imply that whenever
there is an asset in a portfolio that dominates the others in a given sample
(which happens with finite probability even for large samples), then this
portfolio cannot be optimized under any coherent measure on that sample, and
the risk measure diverges to minus infinity. This instability was first
discovered on the special example of Expected Shortfall which is used here both
as an illustration and as a prompt for generalization.
