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Optimal consumption and investment under time-varying relative risk aversion

Author

Listed:
  • Mogens Steffensen

    (Department of Mathematical Sciences - Universitetsparken 5)

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.

Suggested Citation

  • Mogens Steffensen, 2011. "Optimal consumption and investment under time-varying relative risk aversion," Post-Print hal-00796302, HAL.
    • Handle: RePEc:hal:journl:hal-00796302
    DOI: 10.1016/j.jedc.2010.12.007
    Note: View the original document on HAL open archive server: https://hal.science/hal-00796302
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Sascha Desmettre & Mogens Steffensen, 2023. "Equilibrium investment with random risk aversion," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 946-975, July.
    4. 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.
    5. 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.
    6. 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.
    7. Wang, Hang & Hu, Zhijun, 2020. "Optimal consumption and portfolio decision with stochastic covariance in incomplete markets," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. 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.
    9. 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.

    More about this item

    Keywords

    G11; Merton's problem; Hamilton-Jacobi-Bellman equation; Marginal indirect utility; Life-cycle investment;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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