Utility Maximization, Risk Aversion, and Stochastic Dominance

Consider an investor trading dynamically to maximize expectedutility from terminal wealth. Our aim is to study the dependencebetween her risk aversion and the distribution of the optimal terminalpayo. Economic intuition suggests that high risk aversion leads to arather concentrated distribution, whereas lower risk aversion results ina higher average payo at the expense of a more widespread distribution.Dybvig and Wang [J. Econ. Theory, 2011, to appear] nd thatthis idea can indeed be turned into a rigorous mathematical statementin one-period models. More specically, they show that lower risk aversionleads to a payo which is larger in terms of second order stochasticdominance.In the present study, we extend their results to (weakly) completecontinuous-time models. We also complement an ad-hoc counterexampleof Dybvig and Wang, by showing that these results are \fragile", inthe sense that they fail in essentially any model, if the latter is perturbedon a set of arbitrarily small probability. On the other hand, we establishthat they hold for power investors in models with (conditionally)independent increments.[...]