  Consider an agent who enters a financial market on day t = 0 with an initial
capital amount x. He invests this amount on stocks and the money market, and by
day t = T, has generated a wealth W . He is given a convex class of probability
measures (called scenarios) and a real-valued function (or floors)
corresponding to each scenario. The agent faces the constraints that the
expectation of W under each scenario must not be less than the corresponding
floor. We call x acceptable if one can start with x and successfully generate W
satisfying these constraints. The set of acceptable x is a half-line in R,
unbounded from above. We show that under some regularity conditions on the set
of scenarios and the floor function, the infimum of this set is given by the
supremum of the floors over all scenarios under which S is a martingale.
