2010/04/09 by Michael Ludkovski, Ludkovski, Michael, Hyekyung Min +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Economic theories and models #Stochastic processes and financial applications #math.OC #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1004.1489
26 pages, submitted
arxiv created 2010/09/29 · arxiv updated 2010/09/30
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).