Illiquidity Effects in Optimal Consumption-Investment Problems
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).
Cite
@article{arxiv.1004.1489,
title = {Illiquidity Effects in Optimal Consumption-Investment Problems},
author = {Michael Ludkovski and Hyekyung Min},
journal= {arXiv preprint arXiv:1004.1489},
year = {2010}
}
Comments
26 pages, submitted