  We examine Kreps' (2019) conjecture that optimal expected utility in the
classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected
utility for a sequence of discrete-time economies that "approach" the BSM
economy in a natural sense: The $n$th discrete-time economy is generated by a
scaled $n$-step random walk, based on an unscaled random variable $\zeta$ with
mean zero, variance one, and bounded support. We confirm Kreps' conjecture if
the consumer's utility function $U$ has asymptotic elasticity strictly less
than one, and we provide a counterexample to the conjecture for a utility
function $U$ with asymptotic elasticity equal to 1, for $\zeta$ such that
$E[\zeta^3] > 0.$
