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Illiquidity Effects in Optimal Consumption-Investment Problems

  • Michael Ludkovski
  • Hyekyung Min
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    We study the effect of liquidity freezes on an economic agent optimizing her utility of consumption in a perturbed Black-Scholes-Merton model. The single risky asset follows a geometric Brownian motion but is subject to liquidity shocks, during which no trading is possible and stock dynamics are modified. The liquidity regime is governed by a two-state Markov chain. We derive the asymptotic effect of such freezes on optimal consumption and investment schedules in the two cases of (i) small probability of liquidity shock; (ii) fast-scale liquidity regime switching. Explicit formulas are obtained for logarithmic and hyperbolic utility maximizers on infinite horizon. We also derive the corresponding loss in utility and compare with a recent related finite-horizon model of Diesinger, Kraft and Seifried (2009).

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    File URL: http://arxiv.org/pdf/1004.1489
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    Paper provided by arXiv.org in its series Papers with number 1004.1489.

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    Date of creation: Apr 2010
    Date of revision: Sep 2010
    Handle: RePEc:arx:papers:1004.1489
    Contact details of provider: Web page: http://arxiv.org/

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    1. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, 01.
    3. Alessandra Cretarola & Fausto Gozzi & Huyên Pham & Peter Tankov, 2011. "Optimal consumption policies in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 85-115, January.
    4. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    5. Huy�n 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.
    6. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption-Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279.
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