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Optimal consumption and investment under time-varying relative risk aversion

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  • Steffensen, Mogens

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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  • Steffensen, Mogens, 2011. "Optimal consumption and investment under time-varying relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 659-667, May.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:5:p:659-667
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    References listed on IDEAS

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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. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    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 713-736, June.
    4. Aase, Knut K., 2009. "The investment horizon problem: A resolution," Discussion Papers 2009/7, Norwegian School of Economics, Department of Business and Management Science.
    5. repec:kap:iaecre:v:15:y:2009:i:4:p:369-377 is not listed on IDEAS
    6. Li, George, 2007. "Time-varying risk aversion and asset prices," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 243-257, January.
    7. Horace Ho, 2009. "An Experimental Study of Risk Aversion in Decision-making Under Uncertainty," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 15(4), pages 369-377, November.
    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 247-257, August.
    9. Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299, April.
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    Cited by:

    1. Blake, David & Wright, Douglas & Zhang, Yumeng, 2013. "Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 195-209.
    2. Wang, Hang & Hu, Zhijun, 2020. "Optimal consumption and portfolio decision with stochastic covariance in incomplete markets," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Astrup Jensen, Bjarne & Marekwica, Marcel, 2011. "Optimal portfolio choice with wash sale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1916-1937.
    4. Jang, Bong-Gyu & Lee, Ho-Seok, 2016. "Retirement with risk aversion change and borrowing constraints," Finance Research Letters, Elsevier, vol. 16(C), pages 112-124.
    5. 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.
    6. Sascha Desmettre & Mogens Steffensen, 2023. "Equilibrium investment with random risk aversion," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 946-975, July.
    7. Andreas Lichtenstern & Pavel V. Shevchenko & Rudi Zagst, 2019. "Optimal life-cycle consumption and investment decisions under age-dependent risk preferences," Papers 1908.09976, arXiv.org.
    8. Francesco Menoncin & Andrea Modena & Luca Regis, 2022. "Dynamic Tax Evasion and Capital Misallocation in General Equilibrium," Carlo Alberto Notebooks 679 JEL Classification: E, Collegio Carlo Alberto.
    9. Esben Kryger & Maj-Britt Nordfang & Mogens Steffensen, 2020. "Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 405-438, June.

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