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This paper studies the utility maximization problem with changing timehorizons in the incomplete Brownian setting. We first show that the primalvalue function and the optimal terminal wealth are continuous with respect tothe time horizon $T$. Secondly, we exemplify that the expected utility stemmingfrom applying the $T$-horizon optimizer on a shorter time horizon $S$, $S < T$,may not converge as $S\uparrow T$ to the $T$-horizon value. Finally, we providenecessary and sufficient conditions preventing the existence of thisphenomenon.

Horizon dependence of utility optimizers in incomplete models