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Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences

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  • Munk, Claus

Abstract

This paper investigates the dynamic consumption and portfolio choice of an investor with habit formation in preferences and access to a complete financial market with time-varying investment opportunities. An exact and simple characterization of the optimal behavior under general, possibly non-Markov, dynamics of market prices is derived. Relative to the benchmark case of time-additive power utility, habit formation affects the hedge component of the optimal portfolio differently than the speculative component. The quantitative effects of habit formation are studied in three concrete settings. Firstly, a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns is derived. Secondly, with Cox-Ingersoll-Ross interest rate dynamics the optimal strategies are expressed in terms of the solution to a partial differential equation, which has an explicit solution for time-additive utility, but not with habit formation. Thirdly, a new model with both mean-reverting stock returns and stochastic interest rates is studied. Overall, the numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:11:p:3560-3589
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    1. repec:spr:joecth:v:64:y:2017:i:2:d:10.1007_s00199-016-0984-1 is not listed on IDEAS
    2. Holger Kraft & Claus Munk & Frank Thomas Seifried & Sebastian Wagner, 2017. "Consumption habits and humps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 305-330, August.
    3. Xiang Yu, 2011. "An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations," Papers 1112.2939, arXiv.org, revised Aug 2014.
    4. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    5. 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.
    6. Sami Attaoui & Pierre Six, 2014. "Hedging demand and the certainty equivalent of wealth," Economics Bulletin, AccessEcon, vol. 34(3), pages 1742-1750.
    7. Kraft, Holger & Munk, Claus & Wagner, Sebastian, 2015. "Housing habits and their implications for life-cycle consumption and investment," SAFE Working Paper Series 85, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    8. Bruhn, Kenneth & Steffensen, Mogens, 2013. "Optimal smooth consumption and annuity design," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2693-2701.
    9. Zeng, Yan & Wu, Huiling & Lai, Yongzeng, 2013. "Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon," Economic Modelling, Elsevier, vol. 33(C), pages 462-470.
    10. Thomas Q. Pedersen, 2008. "Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution," CREATES Research Papers 2008-60, Department of Economics and Business Economics, Aarhus University.
    11. Haijun Wang & L. Steven Hou, 2015. "Robust Consumption and Portfolio Choice with Habit Formation, the Spirit of Capitalism and Recursive Utility," Annals of Economics and Finance, Society for AEF, vol. 16(2), pages 393-416, November.
    12. repec:kap:rqfnac:v:50:y:2018:i:1:d:10.1007_s11156-017-0627-z is not listed on IDEAS
    13. T. Arun, 2012. "The Merton Problem with a Drawdown Constraint on Consumption," Papers 1210.5205, arXiv.org.
    14. Liu, Xuan & Yang, Fang & Cai, Zongwu, 2016. "Does relative risk aversion vary with wealth? Evidence from households׳ portfolio choice data," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 229-248.
    15. Curatola, Giuliano, 2016. "Optimal consumption and portfolio choice with loss aversion," SAFE Working Paper Series 130, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    16. repec:eee:quaeco:v:66:y:2017:i:c:p:345-358 is not listed on IDEAS
    17. Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.

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