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Risk aversion asymptotics for power utility maximization
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  • Published: 25 November 2010

Risk aversion asymptotics for power utility maximization

  • Marcel Nutz1 

Probability Theory and Related Fields volume 152, pages 703–749 (2012)Cite this article

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Abstract

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).

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Authors and Affiliations

  1. Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland

    Marcel Nutz

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  1. Marcel Nutz
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Correspondence to Marcel Nutz.

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Nutz, M. Risk aversion asymptotics for power utility maximization. Probab. Theory Relat. Fields 152, 703–749 (2012). https://doi.org/10.1007/s00440-010-0334-3

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  • Received: 19 March 2010

  • Revised: 26 September 2010

  • Published: 25 November 2010

  • Issue Date: April 2012

  • DOI: https://doi.org/10.1007/s00440-010-0334-3

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Keywords

  • Power utility
  • Risk aversion asymptotics
  • Opportunity process
  • BSDE

Mathematics Subject Classification (2000)

  • Primary 91B28
  • Secondary 93E20
  • 60G44
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