  Consider an investor trading dynamically to maximize expected utility from
terminal wealth. Our aim is to study the dependence between her risk aversion
and the distribution of the optimal terminal payoff.
  Economic intuition suggests that high risk aversion leads to a rather
concentrated distribution, whereas lower risk aversion results in a higher
average payoff at the expense of a more widespread distribution.
  Dybvig and Wang [J. Econ. Theory, 2011, to appear] find that this idea can
indeed be turned into a rigorous mathematical statement in one-period models.
More specifically, they show that lower risk aversion leads to a payoff which
is larger in terms of second order stochastic dominance.
  In the present study, we extend their results to (weakly) complete
continuous-time models. We also complement an ad-hoc counterexample of Dybvig
and Wang, by showing that these results are "fragile", in the sense that they
fail in essentially any model, if the latter is perturbed on a set of
arbitrarily small probability. On the other hand, we establish that they hold
for power investors in models with (conditionally) independent increments.
