Utility Maximization, Risk Aversion, and Stochastic Dominance

17 Pages Posted: 4 May 2011 Last revised: 22 Sep 2011

Johannes Muhle-Karbe

University of Michigan at Ann Arbor

Mathias Beiglböck

University of Vienna

Johannes Temme

University of Vienna

Date Written: April 10, 2011

Abstract

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 specifi cally, 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 counter example 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.

JEL Classification: G11, C61

Suggested Citation

Muhle-Karbe, Johannes and Beiglböck, Mathias and Temme, Johannes, Utility Maximization, Risk Aversion, and Stochastic Dominance (April 10, 2011). Swiss Finance Institute Research Paper No. 11-18. Available at SSRN: https://ssrn.com/abstract=1813758 or http://dx.doi.org/10.2139/ssrn.1813758

Johannes Muhle-Karbe (Contact Author)

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Mathias Beiglböck

University of Vienna ( email )

Bruenner Strasse 72
Vienna, Vienna 1090
Austria

Johannes Temme

University of Vienna ( email )

Bruenner Strasse 72
Vienna, Vienna 1090
Austria

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