  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).
