Impact of time illiquidity in a mixed market without full observation
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps of a Poisson process with intensity $\lambda$, is observed at the trading dates, and is partially observed between two different trading dates. The problem is a nonstandard mixed discrete/continuous optimal control problem which we face by the dynamic programming approach. When the utility has a general form we prove that the value function is the unique viscosity solution of the HJB equation and, assuming sufficient regularity of the value function, we give a verification theorem that describes the optimal investment strategies for the illiquid asset. In the case of power utility, we prove the regularity of the value function needed to apply the verification theorem, providing the complete theoretical solution of the problem. This allows us to perform numerical simulation, so to analyze the impact of time illiquidity in this mixed market and how this impact is affected by the degree of observation.
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, 2011.
"Optimal consumption policies in illiquid markets,"
Finance and Stochastics,
Springer, vol. 15(1), pages 85-115, January.
- 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," Papers 1107.4210, arXiv.org, revised Apr 2012.
- Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
- Andrew Ang & Dimitris Papanikolaou & Mark Westerfield, 2013. "Portfolio Choice with Illiquid Assets," NBER Working Papers 19436, National Bureau of Economic Research, Inc.
- Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
- 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.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1211.1285. See general information about how to correct material in RePEc.
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.