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The Journal of Wealth Management

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Article

Dynamic Consumption and Portfolio Decisions with Time Varying Asset Returns

Willi Semmler, Lars Grüne and Caroline Öhrlein
The Journal of Wealth Management Fall 2009, 12 (2) 21-47; DOI: https://doi.org/10.3905/jwm.2009.12.2.021
Willi Semmler
is professor of economics at New School for Social Research, New School in New York, NY. semmlerw@newschool.edu
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  • For correspondence: semmlerw@newschool.edu
Lars Grüne
is professor of applied mathematics at Universität Bayreuth in Bayreuth, Germany. lars.gruene@uni-bayreuth.de
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  • For correspondence: lars.gruene@uni-bayreuth.de
Caroline Öhrlein
is a graduate student at Universität Bayreuth in Bayreuth, Germany. lars.gruene@uni-bayreuth.de
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  • For correspondence: lars.gruene@uni-bayreuth.de
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Abstract

In this article, the authors study dynamic consumption and portfolio decisions by using dynamic programming that allows them to compute, with sufficient accuracy, the decision variables and the consumption-wealth ratio at any point of the state space. The dynamic decision problem is first analytically and numerically solved for a simple model with constant returns. Then the authors solve a model with dynamic consumption and portfolio decisions when time-varying returns are calibrated from the low-frequency components of U.S. time series financial data. The implications of the change of investor’s risk aversion, the change of returns, and the time horizon are explored for the consumption decisions, the consumption–wealth ratio, the asset allocation, and the path of wealth.

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The Journal of Wealth Management: 12 (2)
The Journal of Wealth Management
Vol. 12, Issue 2
Fall 2009
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Dynamic Consumption and Portfolio Decisions with Time Varying Asset Returns
Willi Semmler, Lars Grüne, Caroline Öhrlein
The Journal of Wealth Management Jul 2009, 12 (2) 21-47; DOI: 10.3905/jwm.2009.12.2.021

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Dynamic Consumption and Portfolio Decisions with Time Varying Asset Returns
Willi Semmler, Lars Grüne, Caroline Öhrlein
The Journal of Wealth Management Jul 2009, 12 (2) 21-47; DOI: 10.3905/jwm.2009.12.2.021
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  • Article
    • Abstract
    • EMPIRICAL EVIDENCE ON TIME VARYING ASSET RETURNS
    • DYNAMIC CONSUMPTION DECISION: ONE ASSET AND CONSTANT RETURNS
    • DYNAMIC CONSUMPTION AND PORTFOLIO DECISIONS: TWO ASSETS AND TIME VARYING RETURNS
    • CONCLUSIONS
    • APPENDIX 1
    • APPENDIX 2
    • APPENDIX 3
    • ENDNOTES
    • REFERENCES
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  • Editor’s Letter
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