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

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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

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    File URL: http://hdl.handle.net/10.1007/s00780-005-0172-9
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 10 (2006)
    Issue (Month): 1 (01)
    Pages: 121-145

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    Handle: RePEc:spr:finsto:v:10:y:2006:i:1:p:121-145

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Portfolio optimization; liquidity; log-utility function;

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    Cited by:
    1. 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.
    2. S\"oren Christensen & Marc Wittlinger, 2012. "Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs," Papers 1209.0305, arXiv.org, revised Jun 2013.
    3. Paul Gassiat & Fausto Gozzi & Huyen Pham, 2011. "Investment/consumption problem in illiquid markets with regimes switching," Working Papers hal-00610214, HAL.
    4. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    5. 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.
    6. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer, vol. 14(4), pages 363-386, December.
    7. 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.
    8. 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.

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