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Mathematics and Financial Economics

, Volume 13, Issue 2, pp 227–251 | Cite as

Turnpike property and convergence rate for an investment and consumption model

  • Baojun Bian
  • Harry ZhengEmail author
Article
  • 64 Downloads

Abstract

We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property for investment policy. The threshold value only depends on the Sharpe ratio, the riskless interest rate and the discount rate. We show that if utilities behave asymptotically like power utilities and satisfy some simple relations with the threshold value, then the turnpike property for investment holds. There is in general no turnpike property for consumption policy. We also provide the rate of convergence and illustrate the main results with examples of power and non-HARA utilities and numerical tests.

Keywords

Optimal investment and consumption Turnpike property Convergence rate Dual control method 

JEL Classification

D9 G1 

Notes

Acknowledgements

The authors are grateful to the anonymous reviewer whose comments and suggestions have helped to improve the previous two versions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiChina
  2. 2.Department of MathematicsImperial CollegeLondonUK

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