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Optimal consumption and investment under time-varying relative risk aversion

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  • Steffensen, Mogens
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    Abstract

    We consider the continuous time consumption-investment problem originally formalized and solved by Merton in case of constant relative risk aversion. We present a complete solution for the case where relative risk aversion with respect to consumption varies with time, having in mind an investor with age-dependent risk aversion. This provides a new motivation for life-cycle investment rules. We study the optimal consumption and investment rules, in particular in the case where the relative risk aversion with respect to consumption is increasing with age.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 35 (2011)
    Issue (Month): 5 (May)
    Pages: 659-667

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    Handle: RePEc:eee:dyncon:v:35:y:2011:i:5:p:659-667

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Merton's problem Hamilton-Jacobi-Bellman equation Marginal indirect utility Life-cycle investment;

    References

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    1. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    2. Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299.
    3. Markus K. Brunnermeier & Stefan Nagel, 2008. "Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-evidence on Individuals," American Economic Review, American Economic Association, vol. 98(3), pages 713-36, June.
    4. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Horace Ho, 2009. "An Experimental Study of Risk Aversion in Decision-making Under Uncertainty," International Advances in Economic Research, Springer, vol. 15(4), pages 369-377, November.
    6. Aase, Knut K., 2009. "The investment horizon problem: A resolution," Discussion Papers 2009/7, Department of Business and Management Science, Norwegian School of Economics.
    7. Li, George, 2007. "Time-varying risk aversion and asset prices," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 243-257, January.
    8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
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    Cited by:
    1. Marekwica, Marcel & Schaefer, Alexander & Sebastian, Steffen, 2013. "Life cycle asset allocation in the presence of housing and tax-deferred investing," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1110-1125.
    2. Blake, David & Wright, Douglas & Zhang, Yumeng, 2011. "Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion," MPRA Paper 34278, University Library of Munich, Germany.

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