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Mathematics and Financial Economics

, Volume 6, Issue 1, pp 1–13 | Cite as

Utility maximization, risk aversion, and stochastic dominance

  • Mathias Beiglböck
  • Johannes Muhle-Karbe
  • Johannes Temme
Article
  • 222 Downloads

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 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.

Keywords

Utility maximization Risk aversion Stochastic dominance 

JEL Classification

G11 C61 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mathias Beiglböck
    • 1
  • Johannes Muhle-Karbe
    • 2
  • Johannes Temme
    • 1
  1. 1.Fakultät für Mathematik, Universität WienWienAustria
  2. 2.Departement MathematikETH ZürichZürichSwitzerland

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