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Optimal portfolio of low liquid assets with a log-utility function

Author

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  • Koichi Matsumoto

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Abstract

In the real market an asset is not completely liquid. An investor should plan a strategy on the grounds that an asset cannot always be traded. In this paper we consider the classical Merton wealth problem, but the risky asset is not completely liquid. The liquidity is represented by the success rate of the trade and the investor can trade the asset at distributed exponentially random times. We find the value function and exhibit a procedure for an asymptotic expansion of the optimal strategy. Further we reveal some characteristics of the optimal strategy by a numerical analysis. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, January.
  • Handle: RePEc:spr:finsto:v:10:y:2006:i:1:p:121-145
    DOI: 10.1007/s00780-005-0172-9
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    Citations

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    Cited by:

    1. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    2. Paul Gassiat & Fausto Gozzi & Huy^en Pham, 2011. "Investment/consumption problem in illiquid markets with regime-switching," Papers 1107.4210, arXiv.org, revised Apr 2012.
    3. Koichi Matsumoto, 2009. "Dynamic programming and mean-variance hedging with partial execution risk," Review of Derivatives Research, Springer, vol. 12(1), pages 29-53, April.
    4. Huyên Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627.
    5. Salvatore Federico & Paul Gassiat, 2012. "Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets," Papers 1211.1286, arXiv.org.
    6. Kazufumi Fujimoto & Hideo Nagai & Wolfgang Runggaldier, 2014. "Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(1), pages 35-66, March.
    7. Castellano, Rosella & Cerqueti, Roy, 2014. "Mean–Variance portfolio selection in presence of infrequently traded stocks," European Journal of Operational Research, Elsevier, vol. 234(2), pages 442-449.
    8. Paul Gassiat & Huyen Pham & Mihai Sirbu, 2009. "Optimal investment on finite horizon with random discrete order flow in illiquid markets," Papers 0907.2203, arXiv.org.
    9. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    10. Soren Christensen & Marc Wittlinger, 2012. "Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs," Papers 1209.0305, arXiv.org, revised Jun 2013.
    11. repec:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0372-y is not listed on IDEAS

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