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Utility Maximization, Risk Aversion, and Stochastic Dominance


Johannes Muhle-Karbe


ETH Zürich; Swiss Finance Institute

Mathias Beiglböck


University of Vienna

Johannes Temme


University of Vienna

April 10, 2011

Swiss Finance Institute Research Paper No. 11-18

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.

Number of Pages in PDF File: 17

JEL Classification: G11, C61

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Date posted: May 4, 2011 ; Last revised: September 22, 2011

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: http://ssrn.com/abstract=1813758 or http://dx.doi.org/10.2139/ssrn.1813758

Contact Information

Johannes Muhle-Karbe (Contact Author)
ETH Zürich ( email )
Rämistrasse 101
CH-8092 Zürich
Switzerland
+41 44 632 3087 (Phone)
HOME PAGE: http://www.math.ethz.ch/~jmuhleka/
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland
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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