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Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences

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  • Schroder, Mark
  • Skiadas, Costis

Abstract

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based on a preference-independent notion of constrained state pricing. For homothetic generalized recursive utility, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained BSDE. Incomplete market solutions are related to complete markets solutions with modified risk aversion towards non-marketed risk. Methodologically, we develop the utility gradient approach, but for the homothetic case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the BSDE characterizing the solution reduces to a system of Riccati equations.

Suggested Citation

  • Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
  • Handle: RePEc:eee:spapps:v:108:y:2003:i:2:p:155-202
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    References listed on IDEAS

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    Cited by:

    1. Fabio Antonelli & Carlo Mancini, 2016. "Consumption optimization for recursive utility in a jump-diffusion model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, pages 293-310.
    2. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    3. Johnson Kakeu, 2016. "Exhaustibility and Risk as Asset Class Dimensions: A Social Investor Approach to Capital-Resource Economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, pages 677-695.
    4. Maenhout, Pascal J., 2006. "Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium," Journal of Economic Theory, Elsevier, vol. 128(1), pages 136-163, May.
    5. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life-Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    6. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    7. Bhamra, Harjoat S. & Uppal, Raman, 2006. "The role of risk aversion and intertemporal substitution in dynamic consumption-portfolio choice with recursive utility," Journal of Economic Dynamics and Control, Elsevier, pages 967-991.
    8. Hening Liu, 2010. "Robust consumption and portfolio choice for time varying investment opportunities," Annals of Finance, Springer, pages 435-454.
    9. Eric French & John Jones, 2012. "Public pensions and labor supply over the life cycle," International Tax and Public Finance, Springer;International Institute of Public Finance, pages 268-287.
    10. Martin B. Haugh & Leonid Kogan & Jiang Wang, 2003. "Evaluating Portfolio Policies: A Duality Approach," NBER Working Papers 9861, National Bureau of Economic Research, Inc.
    11. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    12. Costis Skiadas, 2015. "Dynamic choice with constant source-dependent relative risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 393-422.
    13. Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.
    14. Hao Xing, 2015. "Consumption investment optimization with Epstein-Zin utility in incomplete markets," Papers 1501.04747, arXiv.org, revised Nov 2015.
    15. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2005. "Portfolio Choice over the Life-Cycle in the Presence of 'Trickle Down' Labor Income," NBER Working Papers 11247, National Bureau of Economic Research, Inc.
    16. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    17. Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    18. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    19. Sbuelz, Alessandro & Trojani, Fabio, 2008. "Asset prices with locally constrained-entropy recursive multiple-priors utility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3695-3717, November.
    20. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    21. Wang, Neng, 2007. "An equilibrium model of wealth distribution," Journal of Monetary Economics, Elsevier, pages 1882-1904.

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