  We study the analyticity of the value function in optimal investment with
expected utility from terminal wealth and the relation to stochastically
dominant financial models. We identify both a class of utilities and a class of
semi-martingale models for which we establish analyticity. Specifically, these
utilities have completely monotonic inverse marginals, while the market models
have a maximal element in the sense of infinite-order stochastic dominance. We
construct two counterexamples, themselves of independent interest, which show
that analyticity fails if either the utility or the market model does not
belong to the respective special class. We also provide explicit formulas for
the derivatives, of all orders, of the value functions as well as their
optimizers. Finally, we show that for the set of supermartingale deflators,
stochastic dominance of infinite order is equivalent to the apparently stronger
dominance of second order.
