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Illiquidity Effects in Optimal Consumption-Investment Problems

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  • Michael Ludkovski
  • Hyekyung Min

Abstract

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).

Suggested Citation

  • Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    • Handle: RePEc:arx:papers:1004.1489
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    References listed on IDEAS

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    1. 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.
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    3. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
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    6. 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, October.
    7. 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, April.
    8. A. M. Il'in & R. Z. Khasminskii & G. Yin, 1999. "Singularly Perturbed Switching Diffusions: Rapid Switchings and Fast Diffusions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 555-591, September.
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    Cited by:

    1. 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.
    2. Michael Ludkovski & Qunying Shen, 2013. "European Option Pricing With Liquidity Shocks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-30.
    3. Fabian Astic & Agnès Tourin, 2014. "Optimal bank management under capital and liquidity constraints," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-21.

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