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We study the analyticity of the value function in optimal investment withexpected utility from terminal wealth and the relation to stochasticallydominant financial models. We identify both a class of utilities and a class ofsemi-martingale models for which we establish analyticity. Specifically, theseutilities have completely monotonic inverse marginals, while the market modelshave a maximal element in the sense of infinite-order stochastic dominance. Weconstruct two counterexamples, themselves of independent interest, which showthat analyticity fails if either the utility or the market model does notbelong to the respective special class. We also provide explicit formulas forthe derivatives, of all orders, of the value functions as well as theiroptimizers. Finally, we show that for the set of supermartingale deflators,stochastic dominance of infinite order is equivalent to the apparently strongerdominance of second order.

On the analyticity of the value function in optimal investment and stochastically dominant markets