We examine Kreps' 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: Thenth discrete-time economy is generated by a scaledn-step random walk, based on an unscaled random variable zeta with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility functionUhas asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility functionUwith asymptotic elasticity equal to 1, for zeta such thatE[zeta 3]>0.
