Satisfying convex risk limits by trading

A random variable, representing the final position of a trading strategy, is deemed acceptable if under each of a variety of probability measures its expectation dominates a floor associated with the measure. The set of random variables representing pre-final positions from which it is possible to trade to final acceptability is characterized. In particular, the set of initial capitals from which one can trade to final acceptability is shown to be a closed half-line . Methods for computing are provided, and the application of these ideas to derivative security pricing is developed.Received: May 2004, Mathematics Subject Classification (2000): 91B30, 60H30, 60G44JEL Classification: G10Steven E. Shreve: Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.Reha Tütüncü: Work supported by National Science Foundation under grants CCR-9875559 and DMS-0139911.