  We consider a single stage stochastic program without recourse with a
strictly convex loss function. We assume a compact decision space and grid it
with a finite set of points. In addition, we assume that the decision maker can
generate samples of the stochastic variable independently at each grid point
and form a sample average approximation (SAA) of the stochastic program. Our
objective in this paper is to characterize an asymptotically optimal linear
sample allocation rule, given a fixed sampling budget, which maximizes the
decay rate of probability of making false decision.
