Illiquidity Effects in Optimal Consumption-Investment Problems

Michael Ludkovski and Hyekyung Min

Papers from arXiv.org

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).

Date: 2010-04, Revised 2010-09
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1004.1489

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