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Abstract: We study the effect of liquidity freezes on an economic agent optimizing herutility of consumption in a perturbed Black-Scholes-Merton model. The singlerisky asset follows a geometric Brownian motion but is subject to liquidityshocks, during which no trading is possible and stock dynamics are modified.The liquidity regime is governed by a two-state Markov chain. We derive theasymptotic effect of such freezes on optimal consumption and investmentschedules in the two cases of i small probability of liquidity shock; iifast-scale liquidity regime switching. Explicit formulas are obtained forlogarithmic and hyperbolic utility maximizers on infinite horizon. We alsoderive the corresponding loss in utility and compare with a recent relatedfinite-horizon model of Diesinger, Kraft and Seifried 2009.



Author: Michael Ludkovski, Hyekyung Min

Source: https://arxiv.org/







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