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Turnpike Property and Convergence Rate for an Investment and Consumption Model

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  • Baojun Bian
  • Harry Zheng

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.

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  • Baojun Bian & Harry Zheng, 2018. "Turnpike Property and Convergence Rate for an Investment and Consumption Model," Papers 1808.04265, arXiv.org.
    • Handle: RePEc:arx:papers:1808.04265
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    References listed on IDEAS

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    1. Robertson, Scott & Xing, Hao, 2017. "Long term optimal investment in matrix valued factor models," LSE Research Online Documents on Economics 69520, London School of Economics and Political Science, LSE Library.
    2. Cox, John C. & Huang, Chi-fu, 1992. "A continuous-time portfolio turnpike theorem," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 491-507.
    3. Jin, Xing, 1998. "Consumption and portfolio turnpike theorems in a continuous-time finance model1," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1001-1026, May.
    4. Paolo Guasoni & Constantinos Kardaras & Scott Robertson & Hao Xing, 2014. "Abstract, classic, and explicit turnpikes," Finance and Stochastics, Springer, vol. 18(1), pages 75-114, January.
    5. Huberman, Gur & Ross, Stephen, 1983. "Portfolio Turnpike Theorems, Risk Aversion, and Regularly Varying Utility Functions," Econometrica, Econometric Society, vol. 51(5), pages 1345-1361, September.
    6. Bian, Baojun & Zheng, Harry, 2015. "Turnpike property and convergence rate for an investment model with general utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 28-49.
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