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In this paper, we extend Kreps' conjecture that optimal expected utility inthe classic Black-Scholes-Merton (BSM) economy is the limit of optimal expectedutility for a sequence of discrete-time economies in initially enlargedfiltrations converge to the BSM economy in an initially enlarged filtration ina "strong" sense. The n-th discrete-time economy is generated by a scaledn-step random walk, based on an unscaled random variable with mean 0, variance1, and bounded support. Moreover, the informed insider knows each functionalgenerating the enlarged filtrations path-by-path. We confirm Kreps' conjecturein initially enlarged filtrations when the consumer's utility function U hasasymptotic elasticity strictly less than one.

Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Markets in Initially Enlarged Filtrations