Illiquidity Effects in Optimal Consumption-Investment Problems
AbstractWe 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).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1004.1489.
Date of creation: Apr 2010
Date of revision: Sep 2010
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-17 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alessandra Cretarola & Fausto Gozzi & Huyên Pham & Peter Tankov, 2008.
"Optimal consumption policies in illiquid markets,"
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
- Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption-Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279.
- Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, 01.
- L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
- Huy�n Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627.
- Paul Gassiat & Fausto Gozzi & Huyen Pham, 2011.
"Investment/consumption problem in illiquid markets with regimes switching,"
- Paul Gassiat & Fausto Gozzi & Huy\^en Pham, 2011. "Investment/consumption problem in illiquid markets with regime-switching," Science & Finance (CFM) working paper archive 1107.4210, Science & Finance, Capital Fund Management, revised Apr 2012.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.