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Optimal consumption and investment with liquid and illiquid assets

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  • Jin Hyuk Choi

Abstract

We consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid risky asset (no transaction costs) and one illiquid risky asset (proportional transaction costs). We fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ODE with an integral constraint. We find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well-posed if and only if there exists a shadow price process. Finally, we describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.

Suggested Citation

  • Jin Hyuk Choi, 2016. "Optimal consumption and investment with liquid and illiquid assets," Papers 1602.06998, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1602.06998
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    References listed on IDEAS

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    1. Dai, Min & Jin, Hanqing & Liu, Hong, 2011. "Illiquidity, position limits, and optimal investment for mutual funds," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1598-1630, July.
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    3. David Hobson & Yeqi Zhu, 2014. "Multi-asset consumption-investment problems with infinite transaction costs," Papers 1409.8037, arXiv.org.
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    6. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    7. Victor Ginsburgh & Michiel Keyzer, 2002. "The Structure of Applied General Equilibrium Models," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262571579, April.
    8. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    9. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    10. 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.
    11. repec:bla:jfinan:v:59:y:2004:i:1:p:289-338 is not listed on IDEAS
    12. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    13. Attila Herczegh & Vilmos Prokaj, 2011. "Shadow price in the power utility case," Papers 1112.4385, arXiv.org, revised Sep 2015.
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    Cited by:

    1. Florent Gallien & Serge Kassibrakis & Semyon Malamud, 2018. "Hedge or Rebalance: Optimal Risk Management with Transaction Costs," Risks, MDPI, vol. 6(4), pages 1-14, October.
    2. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327, arXiv.org.
    3. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "A multi-asset investment and consumption problem with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 641-676, July.

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