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Optimal consumption and portfolio choice with ambiguity

Author

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  • Lin, Qian

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.

Suggested Citation

  • Lin, Qian & Riedel, Frank, 2014. "Optimal consumption and portfolio choice with ambiguity," Center for Mathematical Economics Working Papers 497, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:497
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    File URL: https://pub.uni-bielefeld.de/download/2675321/2901864
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    References listed on IDEAS

    as
    1. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    2. Trojani, Fabio & Vanini, Paolo, 2002. "A note on robustness in Merton's model of intertemporal consumption and portfolio choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 423-435, March.
    3. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    4. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    5. Mark Schroder & Costis Skiadas, 2002. "An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1189-1221.
    6. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    7. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    8. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472 World Scientific Publishing Co. Pte. Ltd..
    9. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    10. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    11. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    12. 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.
    13. Hening Liu, 2010. "Robust consumption and portfolio choice for time varying investment opportunities," Annals of Finance, Springer, vol. 6(4), pages 435-454, October.
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    Citations

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    Cited by:

    1. Ariel Neufeld & Mario Sikic, 2017. "Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty," Papers 1711.03875, arXiv.org, revised May 2018.
    2. Huy N. Chau & Miklos Rasonyi, 2018. "Robust utility maximization in markets with transaction costs," Papers 1803.04213, arXiv.org.
    3. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    4. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    5. Zhou Yang & Gechun Liang & Chao Zhou, 2017. "Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs," Papers 1711.02939, arXiv.org.
    6. Meglena Jeleva & Jean-Marc Tallon, 2016. "Ambiguïté, comportements et marchés financiers," Post-Print halshs-01109639, HAL.
    7. Sara Biagini & Mustafa Pinar, 2015. "The Robust Merton Problem of an Ambiguity Averse Investor," Papers 1502.02847, arXiv.org.

    More about this item

    Keywords

    Robust Finance; Optimal Portfolio Choice; Knightian Uncertainty; Ambiguity; Model Uncertainty;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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