Finance and Stochastics

, Volume 18, Issue 1, pp 75–114 | Cite as

Abstract, classic, and explicit turnpikes

  • Paolo Guasoni
  • Constantinos Kardaras
  • Scott Robertson
  • Hao Xing
Article

Abstract

Portfolio turnpikes state that as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under their myopic probabilities. In diffusion models with several assets and a single state variable, the classic turnpike demonstrates that optimal portfolios converge under the physical probability. In the same setting, the explicit turnpike identifies the limit of finite-horizon optimal portfolios as a long-run myopic portfolio defined in terms of the solution of an ergodic HJB equation.

Keywords

Portfolio choice Incomplete markets Long-run Utility functions Turnpikes 

Mathematics Subject Classification

93E20 60H30 

JEL Classification

G11 C61 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Paolo Guasoni
    • 1
    • 2
  • Constantinos Kardaras
    • 3
  • Scott Robertson
    • 4
  • Hao Xing
    • 3
  1. 1.School of Mathematical SciencesDublin City UniversityDublin 9Ireland
  2. 2.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  3. 3.Department of StatisticsLondon School of Economics and Political ScienceLondonUK
  4. 4.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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